I was going to suggest ozimoron would be the one to ask as that was obviously what he was hinting at but I see he's declined.
There's a lot of debate in Oz about it (most noise coming from the republican side) personally, I think she remained at arms length and it was down to the Governor General. She (and now Charlie) was but a non-political figurehead which to my mind beats the <deleted> out of having a "President".
In fact, this confirms what I thought IMO:
https://www.abc.net.au/news/2020-07-14/what-palace-letters-say-about-queen-role-in-whitlam-dismissal/12454430