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 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.