She certainly did so, in an Alan Bennet play called A Question of Attribution. But Im not sure if she was the first....Are we discounting folk like Mike Yarwood and Pantomime?
Since the Queen has a capital it should refer to Queen Elizabeth I. I don't think she appears in any pantomime I know-unless you mean the Royal family...
I was assuming Queen Elizabeth the Second. The First has been played so many times that memory fades. As to the pantomime thing...a traditional pantomime was a ppolitical play. There are still a few of these around, and they feature characters like the queen and the pope.
And Im saying it depends on which one you see. The pope appears in pantomime (original usage of word) every year at lewes, where he is burnt. Ive seen village hall productions where the queen turns up. OK not the west end, but the tradition lives on.