Toni, you got most of your comments right.
The one you got wrong is that as I said, the GG is her guy on the ground.
He does not decide 'anything'.
HRH has on-going intel about all her countries.
She knew well in advance what that turd Twhitlam was about.
She gave the go-ahead to the GG to sack the moron.
Otherwise the GG just sits around performing his normal day-to-day duties as a matter of course.
The Royals do NOT vote, because they do not want to alienate any of the people, and thereby remaining neutral and retaining the public's favour and popularity, as you pointed out.

//She gave the go-ahead to the GG to sack the moron.//

No, she didn't. You're just making stuff up now.

"The monarch chose not to intervene during the 1975 Australian constitutional crisis, in which Governor-General Sir John Kerr dismissed the Labor government of Gough Whitlam, on the basis that such a decision is a matter "clearly placed within the jurisdiction of the Governor-General". Through her Private Secretary, she wrote that she "has no part in the decisions which the Governor-General must take in accordance with the Constitution"."

http://en.wikipedia.org/wiki/Governor-General_of_Australia#Constitutional_role_and_functions

The old tosspot Curr underlines why we should stand alone.
Alive and active in those days it was clear Labor would be beaten at the next election.
But some thing is very smelly with both the then opposition stopping supply and that drunken old idiots actions.
His drunken rant, he had a few, at the Melbourne cup still reminds me he was the worst GG in a history of bad Englishmen who came here before him, he unfortunately, was Australian

Belly
If His Excellency Sir John Kerr was aussie, how do we stand alone by contrast ? You are yet to score a point, even on this:

"Charlie may have trouble defending his lunch".

"Suggest that you read up about Charles, you might surprise yourself with new found knowledge."

Got your running shoes on, Belly?

What any one of us thinks of Prince Charles is
neither here nor there. The fact remains that
should he become king of Australia he will exert
no political power over our Australian Parliament.

The following link explains:

http://www.spectator.com.au/2018/01/whats-to-gain-from-an-australian-republic/