It ended an extraordinary period in our history, not just during the Queen's life but in the 10 days after her death when waves of unexpected emotion surfaced in Australia and even more in Britain.

Since her death, we have learnt our attitudes to the monarchy are complex.

There is no doubt the Queen was widely respected. Firm republicans including Anthony Albanese expressed their admiration for the monarch in elegant terms. Republicans praised her sense of duty and incorruptibility in a world where both virtues are scarcer than they were.

She embodied public service in what might seem like a selfish era.

It's true there were disgruntled voices on the left who moaned about the coverage of the death but mostly the sentiment has been to respect the Queen in the period of mourning. The Prime Minister said there would be no referendum on the issue of a republic in his first term, meaning there may be no referendum for some time if voters end his lease on The Lodge.

Last week former prime minister Julia Gillard endorsed that view. "I always thought that when the Queen did leave us, that it would cause a period of reflection," she said. "I always thought in Australia, too, it would unleash a new set of reflections about our own constitutional arrangements. But there's no rush. There's time for measured discussion."

Is it too soon to put the reflection into a sharper focus? The question of Australia as a republic (and if so, with what arrangements) is not going away. One of the things we learned from the referendum in 1999 is that these matters are not simple.

Republicans like to put the argument fundamentally as about the unacceptable situation of a proud nation like Australia having a non-Australian as head of state.

They are right. That is an important issue - but there are others, too.

The Westminster system has served Australia well. The question may be how we retain its strengths while transitioning from a monarchy to a republic.

There are all sorts of knotty questions about what powers a president ought to have and how that would affect prime ministerial powers. There is the question of how a president should be chosen - at the suggestion of the prime minister as happens with the Governor-General, or by some form of popular vote. There may be other possibilities. The republican side in 1999 floundered on this inability to unite republicans on the detail of how a republic would work. They would be wise not to make the same mistake.

What we have learnt in the last week or so is there was immense affection for the monarch, if not for the monarchy. It is not clear the popular mood would favour change. There may be an element of "if it ain't broke, don't fix it". Why change an imperfect system for an unknown alternative, would be the argument. All that means there needs to be a lot of thought and a lot of rational, calm debate. We have time to do it. In the meantime, may the Queen rest in peace.