The Queen has to give her permission to suspend parliament (as it is 'her' government), however it was not her decision about whether to say yes or no. She acts on the advice of her Prime Minister, and must do as they say.
Impossible position, much?
I think how it works is the Queen will always deny having had any discretion. If she ever has to reject the 'advice' of her Prime Minister she will say she has been advised that the advice was unconstitutional and therefore she had no option but to reject it.
It's hard to believe that a one-year suspension in modern times would stand, but resolving it would be messy.
It'd be a pretty much immediate constitutional crisis but I don't doubt at all that it'd end up with the head of state getting changed to an elected position. Definitely messy though which is why the tradition stuff works fine for now.
It is actually though. We had a similar situation in Canada a few years back where the PM prorogued parliament for an extended period of time and the Governor-General (our representative of the Crown).
The procedure for formally ratifying a bill is called Royal Assent[1].
An exerpt from the wiki article on it kind of sums up your issue
>Under modern constitutional conventions, the sovereign generally acts on, and in accordance with, the advice of his or her ministers. However, there is some disagreement among scholars as to whether the monarch should withhold royal assent to a bill if advised to do so by her ministers. Since these ministers most often enjoy the support of parliament and obtain the passage of bills, it is improbable that they would advise the sovereign to withhold assent. Hence, in modern practice, the issue has never arisen, and royal assent has not been withheld.
So it's all a matter of tradition and stuff. Theoretically the Queen could go and put her foot down in England or in any other Commonwealth realm that she still technically rules.
That said the common consensus on what would probably happen there is that parliment would essentially immediately have a vote on tossing the queen as head of state, probably write in some elected presidential position or something to do all the stuff that the Queen or her representative used to do then go back to arguing about whatever they were before and the main consequence would be a wasted voting period and having to remove "Royal ____ of ______" from a lot of organizations.
In that case the Governor-General sought, and took, the advice of the Chief Justice.
On the Canadian example from 2008, I note the Wikipedia page says
« It was also at the same time said by Peter H. Russell, one of those from whom Jean sought advice, that Canadians ought not regard as an automatic rubber stamp the Governor General's decision to accept Harper's advice concerning prorogation; Russell disclosed that Jean granted the prorogation on two conditions: parliament would reconvene soon and, when it did, the Cabinet would present a proposed budget, a vote on which is a confidence matter. »
So it seems clear that in Canada, at least, it is not that simple.