We're an independent country!

No, no, NO!
We are speaking of the Queen of Australia. The occupant of the office happens also to be Queen of the UK, Canada and a number of other countries. The Queen of Australia is nevertheless an Australian power. As it happens, the holder of the office has British nationality. So what?

Consider two public companies. They have different shareholders, different businesses, different premises, different managements and different chief executives. However the same person is the non-executive chairman of both companies.

Is one company a subsidiary of the other? No, thought not.

Australia would cease to be independent if the Queen’s (say) Canadian ministers advised her to fire the Governor-General of Australia and appoint someone else, and she took that advice and tried to do so, and (and this is the big one) the Australian courts recognised the new Governor-General. But if Australian courts, minister and other legal institutions refused to accept what had been purported to be done, Australia would still be an independent nation.

Could they refuse? They could and they would, on the grounds that the Queen has been acting unconstitutionally and illegally in exercising her powers on the advice of a foreign government.

Let’s take your analogy:

The non-executive chairman (The Queen) fires the Chief Executive of Australia Corp. (The GG) and appoints her friend Mr. British to be the new CEO. Mr. British attempts to declare martial law but the Minister of State for Defence (Mr. Aussy Poli) refuses, this is treason and he is thrown in jail:

Mr. British (Australia Corp. CEO) appoint a new Minister of State for Defence (Mr. British General). The other’s on the Board of Directors of Australia Corp are getting pissed off and are trying to pass legislation to remove the non-executive chairman, but the non-executive chairman fires the entire Board of Directors because only the Ministers of State are required. By now the shareholders of Australia Corp (The Australian Public) are REALLY REALLY Pissed off, but they have lost pretty much all power (except maybe the power to get shot at while protesting).

And out of the Australian Constitution we see that it is the courts which are bound by the constitution and not the constitution bound by the courts. You can have minor interpretations in the High Court but to blately refuse an entire section of the constitution would be (hence the expression) unconstitutional and therefore illegal. Here’s the quote:

[quote]
5. This Act, and all laws made by the Parliament of the Commonwealth under the Constitution, shall be binding on the courts, judges, and people of every State and of every part of the Commonwealth, notwithstanding anything in the laws of any State; and the laws of the Commonwealth shall be in force on all British ships, the Queen’s ships of war excepted, whose first port of clearance and whose port of destination are in the Commonwealth./

[quote]

So all in all, IF the Queen lost all her marbles she could do this… but she doesn’t have to because the thought experiment proves that Australia is not truely independent.

I wish I’d never got into the public company analogy.

Look, what we have here is a constitutional monarchy under which the Queen of Australia has some apparently very important powers which, by constitutional convention, she can only exercise on the advice of her Australian ministers.

To my mind, if the Queen goes mad and tries to exercise her powers against or without the advice of the Australian ministers, she is attempting to perpetrate a coup d’etat. We can differ about whether she would succeed, whether the courts would accept what she was doing, and whether, if they refused, they would be (a) upholding the Australian constitution and the rule of law or (b) engaging in a revolution.

None of this matters. We could have exactly the same debate if the Queen of Australia were an Australian citizen who was Queen of no other country. Clearly in that circumstance Australia would be independent, however deficient its constitution might be in other respects.

The question is, does Australia cease to be independent merely because the person who has gone mad (a) has British nationality, and (b) is the queen of the UK and several other countries? To my mind the answer is “no”. Nationality is clearly irrelevant, if only because the Australian Citizenship Act could be amended to confer Australian nationality on the King or Queen of Australia as of right, and it would be absurd to suggest that, if Australia is not now independent, that alone would make it independent. And the fact that the Queen is also the Queen of the UK is relevant only if that is in some way connected to her unconstitutional behaviour in Australia.

If a foreign government (e.g. the UK government) were to take it upon itself to advise the Queen as to how to exercise her Australian powers, and if she were to take that advice, and if the Australian institutions were to accept that as legal and effective, Australia would cease to be independent. But that would be equally true if an elected Australian president were to act on the advice of a foreign government. The mere theoretical possibility that this might happen does not mean that Australia is not independent. If it does, there is no independent country anywhere in the world.

I suppose you could argue that a “what if” scenario in which the Queen attempts to exercise Australian powers on the advice of the UK government is slightly more plausible than one in which an elected President does so; I would accept this. That would suggest that Australian independence is slightly more vulnerable than it would be if it were a Republic, or had a native monarchy. But it is still independent.

I’ve highlighted the phrase above because I think it explains why we can hold these opposing viewpoints.

Queen Elizabeth (of the UK, Australia etc.) speaks weekly to the UK Prime Minister. She opens the UK Parliament. She does not ‘interact’ with Australia in the same way.
If she were to take some dramatic action in Australia, she would presumably have consulted with the British Government first.
So technically Australia is not ‘independent’.

But as UDS points out, all this is bound by ‘convention’.
The Queen does not involve herself in UK politics (apart from those little chats). Her speech to Parliament is written for her by the current Prime Minister. It is clear from recent UK history that she does not have a consistent political strategy (neither apparently do our politicians, but that’s another thread!).
So Australia is effectively independent.

Perhaps it’s similar to the Commonwealth and Zimbabwe. If there is electoral fraud, the Commonwealth can … threaten to expel Zimbabwe. Ooooh!