Under the Australian Constitution, who will become Australia's Head of State if the British monarchy is suddenly dissolved or overthrown and Britain becomes a republic?
The Queen of Australia, i.e. Elizabeth II. The Commonwealth realms have the same monarch and the same line of succession, but as a legal matter they are separate monarchies of separate and independent countries. Elizabeth II's title as Queen of Australia is not a result of her title as Queen of the UK.
This can be seen in some articles of Australian legislation, like the Succession to the Crown Act 2015. That act gives its purpose as
to change the law relating to the effect of gender and marriage on royal succession, consistently with changes made to that law in the United Kingdom, so that the Sovereign of Australia is the same person as the Sovereign of the United Kingdom.
By implication, without that act of the Australian Parliament, a change to UK succession made by the UK Parliament could result in the Sovereign of Australia being different from the Sovereign of the UK.
It's also come up in a few citizenship-related court cases (e.g. Sue v Hill, Nolan v Minister for Immigration and Ethnic Affairs), in which someone who was a citizen of another Commonwealth realm made them an alien or a citizen of a foreign power. The Australian courts have cited R v Foreign Secretary; Ex parte Indian Association, a case brought in England to enforce obligations of treaties between the UK and Canadian Indians from the 18th century. The English courts responded by saying that the position that the Crown was a single indivisible monarchy was no longer tenable in 1982, and that the position had been split up. The Canadian treaties with the Queen of Great Britain were now obligations of the Queen of Canada, and had to be enforced in Canadian courts. While the Australian Constitution is interpreted by Australian courts (not British ones), they have agreed with the English analysis.
The Australian Constitution may declare that the Crown refers to the Queen's heirs and successors in the sovereignty of the UK, but the Queen in question was Victoria, and there have been some major changes since then. Australia is now an independent, sovereign country, and its monarchy is no longer legally identical to that of the UK. They may share a monarch and a line of succession, but that's only because the parliaments of the two countries decided to coordinate.
Section two of the Australian Constitutional Law reads as follows:
(2) Act to extend to the Queen's successors
The provisions of this Act referring to the Queen shall extend to Her Majesty's heirs and successors in the sovereignty of the United Kingdom.
As made clear in this last part, it is presupposed that the Queen and her heirs will be 'successors in the sovereignty of the United Kingdom', but as I read it, it is the sovereign of the United Kingdom the rule of succession refers to.
There is nothing clear here.
Therefore, because of the problems that might occur and the boundness of the idea of the Commonwealth to the british monarchy, I would speculate that Australia would rather alter its constitution (and may it only be omitting the bolded part), than having this ambiguity remain.