I've personally never seen Doctor Who, but this still made me chuckle a few times.
I think my major gripe with this is, even though you're going for a "floating hands" style, it's pretty lazy animation overall. The eyes aren't animated and they don't have mouths, which really breaks the feel in my opinion. If you had at least given them some life in the eyes, which is often where your audience is looking, I could have overlooked the lack of lip sync... but with them being so static and frozen I end up feeling bored, because there's no contrast in the acting, I have to rely on the voice acting which (while pretty decent) did not carry me the whole way.
I think the gags and the delivery are fine. The humor is there and for someone who doesn't watch the show you still had me chuckling... but this could have been something so much better!