It certainly is. The syntax of the Australian Constitution sits firmly within British conventions of monarchical behaviour, buttressed by the Acts of Westminster and the Australia Acts.
We are an independent nation in custom and law. If Her Majesty tried to do anything, she would be ignored. If she sued, the High Court would politely explain that her role is entirely ceremonial and that Parliament is the supreme source of executive and legal power in Australia.
The principle that Parliament is supreme over Crown was established in British law before Australia was colonised. It's pretty well-accepted at this point that the royals have no power.
The Queen did not dissolve Parliament. (Neither did the Governor-General during the Whitlam dismissal.)
The Queen has never, and cannot, do so in right of Australia, because her powers are irrevocably and excludably delegated to the Australian Governor-General.
In terms of dissolving any Parliament nominally under her sovereignty, it can only be done by the Queen or a Governor-General upon advice. The Queen can't do it of her own initiative. Neither can the Governor-General. They have to be told to do it by the Government of the day.
The Queen herself did nothing.