(I was reacting to your thread title, which says shoot at your wedding. But now you said "shoot your wedding"--which is the expression I am used to hearing as well.)Interesting point.... This expression is a hold over from my days as a photojournalist. It is common there, and as well in the wonderful world of weddings. It is used all the time in normal photographer banter.
We use it all the time to say : Shoot someone's wedding. Or if you are with someone shooting for you, you might say, seeing a photo... shoot that! Or you might even say to tell someone that you are heading to your assignment, "I am heading to my shoot."