Have you a calender? I think this has already been signalled but it looks as if it has not yet been added.
Is that really a natural construction for you?
I have heard of conservative British English speakers who use such constructions but I'm not sure whether I've ever actually met a real live speaker myself who does so.
In other words, are you notifying this because this is the first thing that came to your mind and you were disappointed that it was not accepted, or because you are trying to "test the borders"?
(It's added now, but I'm still curious whether you're trying to solve a real problem or a non-problem.)
Yes "that is really a natural construction for me" I must be one of your conservative British English speakers. That would surprise my friends !
"Have you..." instead of "Do you have..." is regularly used in Ireland, too.