As Mike says, Queen Anne" is a pure "collectorism". It has no proper definition. I've always taken ti suggest a sidelock, turn-off barrel pistol of the type popular during her reign, which ended in 1714. Pistols of that type continued to be made into the 1730s. This example is more properly called a "box lock pocket pistol" which is exactly what it is.
One thing that modern collectors tend to forget is that gunmakers weren't artists (though some were very artistic). They were tradesmen, trying to make a living. Robert Wogden, for instance, lived over the shop. Twigg's name commonly forged because he was well known. DeWitt Bailey once pointed out that there was a big market in "used" up-market guns and that some extremely good Birmingham makers literally made "fake" used guns... because they were easier to sell. This one isn't even that. Its a mid-quality pocket pistol, of which tens of thousands were made, marked with a spurious name because it was presumed, almost certainly correctly, that the potential buyer had probably never seen a real Twigg gun and wouldn't be able to tell the difference. Practically everyone above the social class of day laborer carried pocket pistols in the 18th and early 19th century but, unless you were a member of the landed gentry or worked in such a household, you probably never saw any of the products of the great London makers.