Crossbencher waiting for Wentworth result

Central Alliance MP Rebekha Sharkie is putting Prime Minister Scott Morrison's ability to provide a "good, stable government" under the microscope until the Wentworth by-election.

The crossbencher says she will not support a no confidence motion in the government while Malcolm Turnbull's previous seat remains vacant, after the former prime minister quit politics over the recent bitter leadership battle.

Centre Alliance would support a motion to refer Home Affairs Minister Peter Dutton to the High Court over his eligibility to sit in parliament due to his financial interest in childcare centres, Ms Sharkie added.