When John Key became the first New Zealand Prime Minister to speak in the Australian Parliament, he must have felt like a visitor to an unhappy house. His host, Julia Gillard, has become so unpopular that there is talk her party could reinstate Kevin Rudd, deposed as Prime Minister a year ago on Friday. This country can only watch her difficulties with regret.

Ms Gillard made a warm impression on a rare (for Australian Prime Ministers) state visit here in February. She came in the wake of the first Canterbury earthquake and the Pike River disaster and spoke of us as family. The following month, she returned to attend the Christchurch memorial service for the city's devastating February 22 earthquake.

With her that day was Opposition leader Tony Abbott. When Mr Key alluded to the natural calamities in both countries over the past year, the sentiment would have briefly united the federal Parliament. But the ties between our two Governments usually depend on the chemistry at the top and right now it could not be better.

Mr Key would be doing this country a disservice if he did not give Ms Gillard due credit for the state of the relationship, even at risk of stepping into a domestic political minefield. When a government is unpopular, the public is loath to hear anything positive said about it. Conversely, when its leader is popular, he can do no wrong.

At home, Ms Gillard has always been labouring under the circumstances that put her in power. Mr Rudd had run into hostility over his proposed mining tax and was dumped on the strength of opinion polls that suggested Labor would lose last year's election. In the event it very nearly lost under Ms Gillard too, scraping back when she was able to negotiate a post-election deal with three independent MPs.

Now Ms Gillard is being damned for a tax of her own, on carbon emissions. She is pressing ahead with a carbon tax despite public opinion against it, confident she can hold the Government together and the country will get used to the tax in the two years remaining to the next election. Meanwhile, the polls are worse for her and the Government than they were when Mr Rudd was replaced and, despite his denials, Mr Rudd must be harbouring hope of a return.

Ms Gillard used her press conference with Mr Key to advance the case for her carbon tax, pointing out that New Zealand has introduced an emissions trading scheme that effectively put a price on carbon. Mr Key in turn waded further into the issue than he might have done had Ms Gillard not already done so much for the transtasman relationship.

He said New Zealand and Australia had to work together on climate change and a scheme allowing carbon credits to be traded across the Tasman "makes sense". It certainly would. The wider the market for buying and selling emission rights, the more carbon credits are likely to be available and the more likely it becomes that the market can put a fair price on atmospheric damage.

But a carbon tax is a long way from a market price. A tax is an arbitrary price set by politicians at a rate they think their voters might accept. The Key Government put a ceiling on the price the market can set when it amended the emissions trading scheme introduced by Labour in 2008. Both countries are moving tentatively on climate change, conscious that the subject has faded from public attention since the global financial crisis.

Closer economic relations dominate all dealings between the two countries but their Prime Ministers had much else to discuss yesterday. Afghanistan and Fiji pose joint global and regional concerns but not much difference of opinion. The Anzac bond is in good heart at present. New Zealand has more than a passing interest in Ms Gillard's struggle.