https://en.m.wikipedia.org/wiki/1975_Australian_constitution...
In principle this power still exists. Whether Charles could pull off the same trick depends on the political situation on the ground.
I'm old enough to remember it and remember a statement from the palace saying something like "The Queen is watching events in Australia with interest" but I don't think she took an active part.
I quick search reveals this. I don't know this site but if true then some letters seem to confirm the above. She told the GG to obey the Australian Constitution.
https://constitution-unit.com/2020/07/16/palace-letters-show...
https://en.wikipedia.org/wiki/Alleged_CIA_involvement_in_the...
It's true that the palace was involved in discussions with the GG to a greater extent than most Australians though was acceptable though.
However this was before the 1986 Australia Act which cleared up the ambiguity around that.