I’m not going to lie, I don’t actually think a live-action crossover would be a very good idea. I love them both dearly, but I’m not sure these are two great tastes that would taste great together.
Incidentally, Doctor Who is pretty good at presenting new jumping-on points - having to replace your lead actor every few years has its advantages. This new season would be a great place to start, and the episodes are weird in a uniquely DW way that would give you at least a taste of the insanity you’d be in for.