I painted a couple of T shirts with Doctor Who subjects on them. One is with David Tennant (the 10th Doctor), the other with Peter Capaldi (12th, his last season will be aired soon).
As a painter and a fan of Doctor Who, why shouldn't I make my own T shirts or gadgets? Of course I do it just for myself and my wife. Everything about the Doctor is copyrighted and you can't use it for sales!
(Can't find a photo of my Capaldi T shirt, and the shirt itself is somewhere between the summer clothes ^^)