New prime minister Scott Morrison will enter his first sitting week in Canberra as leader buoyed by the latest Newspoll showing he leads his rival Bill Shorten 42 - 36 as preferred PM.

But the Coalition still trails Labor 44-56 in the key two-party preferred result, according to the Newspoll published on Monday, suggesting voters are still punishing the government for dumping Malcolm Turnbull.

The opposition is planning to target the Coalition's internal division in Question Time this week, singling out MPs who pledged loyalty to Mr Turnbull days before they voted in favour of a leadership spill.

Labor will also move to test the government's hold on the House of Representatives.

With the departure of Malcolm Turnbull, the government has lost its slim one-seat majority and could be caught out by tactical maneuvers on the floor of parliament.

Labor's manager of opposition business Tony Burke said they would try to pass a motion to refer Home Affairs minister Peter Dutton to the High Court over an alleged constitutional problem, but are pressuring the minister to refer himself.

Nationals deputy leader Bridget McKenzie told the ABC it was a decision for Mr Dutton whether he referred himself to the High Court.

She said the Liberals' recent defeat in the NSW state by-election in Wagga Wagga showed voters were angry with the political games in Canberra.

"It reflects on how parliamentarians and parliament itself are being perceived. When we are not talking about the things that matter to real people in their communities, they rightfully punish us," she said.

- with AAP