In late June, visiting Singapore to ink the Comprehensive Strategic Partnership (CSP) with Prime Minister Lee Hsien Loong, then Australian Prime Minister Tony Abbott dropped by at the Religious Rehabilitation Group's centre in Geylang Road.

There, chatting with two imams, the former Oxford boxing Blue, known for never meeting a punch he couldn't block with his face, showed an unusually sensitive side.

"I once trained to be a Catholic priest," he told the two Muslim preachers quietly, after hearing how Singapore tries to put radicalised youth on the correct religious path. "I know very well the phenomenon of young people trying to do their best for God and flipping over into something dangerous."

The CSP spans some 80 initiatives across multiple fields, covering cooperation in areas such as anti-terrorism, investments, employment and, in particular, defence. It ties down a relationship whose intensity is not often recognised, or evident to all.

It stands for the record that the initiative came from Mr Abbott and was the most successful, and promising, of his Asia-facing initiatives. Indeed, the scale of his ambition was such that he wanted his nation's ties with Singapore at the same intensity as those with New Zealand.

To understand the significance of this initiative, you must note that Mr Abbott - who was unseated this week in a party coup - came into office promising "more Jakarta, less Geneva".

Ties with Jakarta have waned significantly since President Joko Widodo took power. Certainly, they are nothing like those that marked the heydays of the Kevin Rudd- Susilo Bambang Yudhoyono lovefest. Some years ago, Canberra might even have considered Kuala Lumpur to make the offer of a close strategic partnership.

THE MERLION AND THE AUSSIE LAMB

That Mr Abbott came to Singapore for the grand bargain speaks for something. Clearly, just as Asia is taking stock of itself, the world is reassessing Asia as well, and making some decisive conclusions.

Still, it takes a particular type of leader to have the strength of conviction to go by his gut instinct, rather than the multi-hedged position papers submitted by bureaucrats and think-tank types. Then United States President George W. Bush, the choker-on-pretzels, displayed such a quality in 2005, when he signed the landmark civilian nuclear deal with India.

"The second-largest Muslim population in the world, and no Al-Qaeda," an impressed Mr Bush reportedly told his wife at the time.

Today, the US and India are building one of the most serious strategic alliances taking shape in the world. Indeed, thanks to this, the new buzzword for the Asia-Pacific is "Indo-Pacific".

Mr Abbott - whose most recent gaffe was to eat a raw onion, skin and all, while on a farm visit - was perhaps going against the grain in some ways when he asked the Merlion to lay down with the Aussie lamb. Even as recently as last month, Mr Peter Varghese, the widely admired head of the Australian foreign service, described Indonesia as "the country that matters most to us in South-east Asia".

I say this because - even though Australia was perhaps the first nation to recognise independent Singapore - there have always been two types of Australian when it comes to perceptions about the smaller island.

The first affected a dim view of the Republic and its all-too-serious citizens focused on growing their economy, comparing it unfavourably with Australia's laid-back culture and freewheeling democracy.

In contrast, the right-wing in Australia had a grudging admiration for Singapore, perhaps seeing in it a nation they would like their own country to resemble in some ways.

And still, there is more. The partnership with Singapore also underscores how much Australia has snuggled up close to Asia since the turn of the century.

AUSTRALIA'S SHIFT TO ASIA

Australia was settled in the late 18th century as a British colony, and the first legislation passed there was for a White Australia policy. That instantly set up Asia as a "threat". Indeed, not too long ago, some Australian strategists made a good living by even talking up a threat from India's plans for a blue-water navy, before they switched their attention to China's regional ambitions.

However, as the saying goes, geography is destiny. In the 1970s, the White Australia policy was formally ended, and the country began its journey towards its current reality as a throbbing, multiracial entity with a large ethnic Asian population.

How Australia's racial profile had changed came to me starkly some years ago, while I was covering South Asia for this newspaper.

In early 2010, New Delhi newspapers screamed about a series of alleged racial attacks on Indians on the continent. "The buzzard of Oz", said a headline in Hindustan Times, days after the Mail Today tabloid portrayed Victoria state police as the Ku Klux Klan. There were 120,000 Indian students in Australian universities, and some parents were calling their children home.

Checks revealed a more nuanced picture. Some of the attacks involved Lebanese students attacking Indians who had undercut them on pay and were prepared to work longer hours. In a few cases, young Indian men had hit successfully on bored Australian women, setting up a confrontation with jealous husbands. This wasn't exactly racial.

This is not to imply that Australia doesn't have its share of rednecks. There are plenty around. But an undeniable commitment to multiracialism and tolerance has seeped into society. When a Muslim gunman held people hostage at a Sydney cafe in December last year, one of the trending Twitter threads was #illridewithyou, as Australians reached out to Muslim compatriots to assure them that there would be no xenophobic backlash.

As much as its changing social face, Australia's strategic interests are also fully enmeshed with Asia now. It was Asean's first dialogue partner. With first Japan, then China, supplanting Europe as its top trading partner, its economic interests are rooted in the region as well - hence its emphasis on freedom of navigation in the seas and in the air.

That's where things are today - hence its principal external worry: What if all this went horribly wrong?

Now that Mr Abbott's gone, eyes have turned to his successor, Mr Malcolm Turnbull, to see what direction he will take to meet the challenges of the day. The Australian Defence White Paper, due out soon, will be read carefully, particularly in the light of China's own Defence Paper, put out recently.

Foreign Minister Julie Bishop's influential presence - she was the kingmaker in the coup - signifies continuity in foreign policy.

Singapore itself might not have much to worry about. When Mr Abbott brought the CSP to the Cabinet earlier this year, it was said to have "gone through on the nod".

As a former investment banker, Mr Turnbull is even more familiar with Singapore than Mr Abbott was. It also helps that his son is employed in the financial industry here - one of 25,000 Australians living on the island. The relationship is poised to strengthen when PM Lee heads to Australia in the middle of next year.

Still, some differences in emphasis are perhaps inevitable.

Mr Abbott had worked himself very close with Japanese Prime Minister Shinzo Abe. It looked for a time as though Canberra would buy Japanese submarines as part of that strategic embrace. However, the man tipped to replace Mr Kevin Andrews, Mr Abbott's defence minister, is Mr Christopher Pyne, who is from South Australia. Given the slowing economy of that region and the emphasis on jobs, it is conceivable that Mr Pyne's instinct might be to buy the submarines from European manufacturers which offer more offsets - something that would help the local economy. That would weaken one strategic embrace in the region.

On the other hand, ties with the US might well improve, especially in terms of issues such as climate change. Mr Abbott had a mixed relationship with Washington. Even though they worked closely on strategic issues, including the battle against the Islamic State in Iraq and Syria, he had lost confidence in President Barack Obama's competence in managing the security challenges of the day, particularly in Iraq and Syria.

The really interesting element will be how Mr Turnbull approaches China.

Mr Abbott had built up his Asian connections without unduly raising concern in Beijing. Just this month, Mr Andrews said in New Delhi that he was keen for Australia to join this year's Exercise Malabar - a naval exercise in the Bay of Bengal involving the navies of the US, Japan and India. This week, the Australian and Indian navies are holding their first bilateral exercises in the Bay. China, not without reason, sees some of these moves as being aimed at itself.

Without compromising the basic security matrix, Mr Turnbull might well take a more cautious and balanced approach towards China that should cheer the mainland.

Still, as Ms Alex Oliver of the Lowy Institute in Canberra noted this week: "China's latest round of land-reclamation activity in the South China Sea might well stiffen Mr Turnbull's stance on this issue."

The many ways Australia has integrated with Asia aside, its fractious, intrigue-filled politics forms an aspect of its national character that will separate it from large parts of Asia for a while.

Most Asian states, particularly in East Asia, tend to plan their transitions carefully. They understandably look askance at a nation that frequently shuffles to power people other than those who won the mandate. Who in the world wants to order an Angus steak only to look down at their dinner plate an hour later to find that the restaurant has slyly switched their beef for a spatchcock?

Australians should be aware too that, at a time of strategic overreach by more than one regional power, most Asians realise they have to chart their courses by carefully feeling the stones under their feet.

It doesn't help to have the uneasy feeling that a fellow traveller, while a great chum now, is capable of switching sides any time.