[mjw1007]

See https://en.wikipedia.org/wiki/1975_Australian_constitutional... for an example of a Governor-General acting without the advice of their ministers.

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.