As I understand it, if the Queen indicated that she wished to abolish the monarchy and the government indicated that it wanted to retain the monarchy, it would create a situation where the Queen was not “acting on the advice of her ministers”, which would pose a constitutional crisis in and of itself.
It’s not illegal for Parliament to do anything. The taboo on discussing the monarchy is only really in place out of respect (that, and the fact that the monarchy has no right of reply would make it somewhat discourteous). The formal barriers, such as they are, could easily be overturned.
True. But the incumbent officeholder has spent 50 years building political capital and resisting the temptation to use it. What argument would monarchists have to retain the monarchy if the (well-respected) monarch herself wants to get rid of it?
Simple: it can’t be illegal for MPs to introduce themselves, because that would violate the doctrine of supremacy. Though as noted they wouldn’t even be violating the Act if they got permission to talk about it first.
Two arguments:
First, that it is not for one person to decide the basic constitutional structure of the country. Her views are certainly worthy of respect, but are not determinative. If the people believe that a monarchy is preferable, that is their decision to make.
Second, even if the people decide to go republican, there will be a lengthy debate as to the nature of the government that will be created. Fundamental change can take time and considerable political capital. One person does not get to direct that process, and until it has occurred, the basic constitutional structure of the country remains as is.
I don’t think it can be denied that the Queen turning republican wouldn’t shake the system to its core, though. It could survive, but it would have a powerful enemy in the former Head of State.
You’re so much more succinct, Freddy! 
So if the Queen decided to take an extended hike on the Appalachian Trail, go into seclusion in a Tibetan monastery, or developed a medical condition that prevented her from saying or writing “I assent” what would happen to the Canadian government? Would it grind to halt? Is there an alternative means for the government to function when the Queen is not available?
Could Canada unilaterally appoint someone else to serve as Queen of Canada with less difficulty than converting to a republic? Could they call the actors’ union and hire someone to put on a crown and say “I assent”?
Canada can of course change the Canadian monarchy unilaterally. As a sovereign nation, we do not need the British Parliament to do anything, and the British Parliament has no legislative authority over Canada.
However, under our constitutional amending formula, changes to the Canadian monarchy require unanimous consent, as set out in the Constitution Act, 1982:
If HM is unavailable, the terms of the Regency Act (UK) would come into force, and Prince Charles would be appointed as regent.
Thanks!
But would that solve Canada’s problem? if . . .
. . . would Canada not need its own regency legislation?
If I remember correctly, when the line of succession was altered after 2011 to allow absolute primogeniture, the Canadian Parliament merely resolved that the Monarch of the United Kingdom is automatically Monarch of Canada. So it’s in Canadian law that they automatically share our Head of State.
It remains in their power to change this if they wish.
Edit: thinking about it, I don’t think the Regency Acts apply to any country apart from the UK. All other countries have Governors-General, and so there’s no question of the Head of State being underage/senile/ill etc. It only matters to the UK. So the Queen could go senile tomorrow, Charles would become Regent of the UK, but the Queen would remain Queen of the UK, and Queen of all other Commonwealth Realms.
They do in New Zealand (its constitution explicitly says any UK regent is automatically the NZ regent) and I think also a couple of the other Pacific island realms.
I don’t know what the regency rules are, but the line of succession is different in Aus for some edge cases.
. I think this is the answer to the Regency Act question, but I’m not sure.
No, it does matter to Canada because the Gov Gen’s term is five years. Only the Queen can appoint a new Gov Gen. If the Queen is incapable of acting, there has to be someone to act in her name, on the advice of the Canadian PM, to appoint a new Gov Gen.
I would assume that issue would arise in the other Commonwealth realms that have a Gov Gen.
There are also a few other things that only HM can do under our Constitution, like appoint additional senators to break a stalemate in the Senate.
Is this actually the law or just a tradition? The GG’s letters patent say that “appointments to the Office of Governor General and Commander-in-Chief in and over Canada shall be made by Commission under Our Great Seal of Canada” and that the GG can “[seal] all things whatsoever that may be passed under Our Great Seal of Canada.” The Constitution doesn’t seem to mention the actual appointment of a Governor General, it just presumes that there is one.
But the Regent is not the head of state. If the Queen of the UK becomes a stranger to reason and the UK Regency Act takes effect, the Queen is still the Queen of the UK (and of Canada). And presumably the UK regency legislation can only allow the Regent to exercise the Queen’s functions with respect to the UK, not with respect to Canada. That would require Canadian legislation, surely?
I’m pretty sure that it’s not. The Constitution of Australia explicitly provides that those of its provisions which refer to the Queen “shall extend to Her Majesty’s heirs and successors in the sovereignty of the United Kingdom”. This could be amended, but so far it hasn’t been, and it would need to be, if there were any possibility that a different person might occupy the thrones of the UK and Australia.
So far as I know, the only Australian legislation dealing with succession to the crown is the Succession to the Crown Act 2015 (Cth) (and similar Acts of each state). That legislation provides for gender-neutral succession to the crown and removes the bar on the monarch marrying a Catholic, and it was passed to parallel similar legislation being enacted in the UK, so its purpose was to keep the succession rules the same in both countries, not to introduce different succession rules.
And, on a nitpick, I don’t think this is right.
The position of the Canadian government is that the monarch of the UK is automatically monarch of Canada, but I don’t think the Canadian Parliament has ever passed a resolution to this effect. With regard to absolute primogeniture, the Canadian Parliament enacted the Succession to the Throne Act 2015, which noted the UK legislation on this point, and assented to it.
If the Queen becomes a Republican…
… she’d probably vote for JEB. I just can’t see her voting for Rubio or Cruz, and certainly not for Trump.
So does parliament have immunity from prosecution for statements made in parliament? Like for example I know that certain subjects are like hate speech can be prosecuted in the UK are members of parliament exempt for such laws?
Speeches in Parliament are protected as Privilege, yes, so MPs cannot be arrested for slander or libel, although they can of course incriminate themselves and others for things like murder or corruption.