The sudden coup by Mr Malcolm Turnbull to become Australia's Prime Minister appears to have given a boost to the ruling coalition, which last night recorded a better-than-expected win in a local election in Western Australia.

In a special election in the seat of Canning, Mr Turnbull's Liberal party was set to defeat the Labor candidate by 56 per cent to 44 per cent.

The election, to replace a local Liberal MP who died of natural causes earlier this year, was seen as the first indicator of whether Mr Turnbull's appointment would assist the fortunes of the ruling coalition.

The result marked a sizeable 6 per cent swing against the Liberal party but this was better than the 10 per cent swing forecast by recent polls before former prime minister Tony Abbott was ousted on Monday night.

Analysts said both the coalition and the opposition, which improved its standing, would be heartened by the result. "It is a pretty clear result," election analyst Antony Green told ABC News. "It is a result which is a bit neutral for everybody."

The winning Liberal candidate in Canning, Mr Andrew Hastie, a former Australian special forces soldier, ran a tough anti-drugs campaign but insisted his win was due to local issues rather than the dramatic events last week in Canberra. He paid tribute to both Mr Abbott and Mr Turnbull.

"The people of Canning don't care about Canberra politicking or tricky games ," he said last night.

Mr Turnbull, a popular former investment banker and lawyer, defeated Mr Abbott in a party-room ballot following a run of dismal polls for the ruling coalition.

In the first national survey on Friday since Mr Turnbull became Prime Minister, a Galaxy poll found his coalition led the opposition by 51 to 49 per cent. Just two weeks ago, the coalition trailed the opposition by 46 to 54 per cent.

The Prime Minister is expected to unveil his new Cabinet today. He is expected to appoint Mr Scott Morrison as the new Treasurer and is reportedly set to create a new minister for innovation.