Australia's foreign minister Julie Bishop has said she looks forward to working with New Zealand's new Labour-led Government - despite saying in August she would have serious trust issues if Labour was in power.

Bishop said earlier this year that "should there be a change of Government, I would find it very hard to build trust with those involved in allegations designed to undermine the Government of Australia".

Her comments followed the revelation that Labour MP Chris Hipkins had been involved in outing Australia's deputy Prime Minister Barnaby Joyce as a New Zealander by descent.

Under Australian law citizens of other countries are ineligible for Parliament. The Australian High Court is set to determine Joyce's political fate in the next few days.

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Jacinda Ardern strongly denied any knowledge of the incident and said she had spoken sternly with Hipkins over the matter.

And she hit back at Bishop, saying the Foreign Minister's comments were "highly regrettable" and she had contacted the Australian High Commission to register her disappointment.

Bishop later said she took Ardern at her word that she had not known anything about the matter.

But following tonight's announcement that Winston Peters and NZ First would form a coalition with Labour, commentators again raised the issue.

Speaking to Australia's Channel 9 tonight Bishop said her party had a "very strong and deep relationship with New Zealand" and she looked forward to working with the new government.

Asked if she could trust Ardern, Bishop said the Labour leader had explained in August that Hipkins' conduct was "wrong, it was unacceptable and it should never have happened and that he shouldn't have become involved.

"And I accepted her explanation and I agree with her absolutely."

In a series of tweets following the announcement Bishop also rubbished opinion pieces that claimed she could not work with Ardern.

She also retweeted Australian Prime Minister Malcolm Turnbull's congratulatory message to his New Zealand counterpart.

Bishop has been the brunt of jokes online tonight following NZ First's decision.