It's a shame honestly. I'm not saying it out of sexism, I'm not saying it because I think women can't act, I'm saying this because it takes away the original premise of the show. Dr Who appeals to nerdy guys who want to see a fellow nerdy guy fight aliens, it's not that hard honestly, Matt Smith is a plain example.
Steven Moffat, the guy who pretty much made Dr Who the pop culture phenomenon quit alongside with Peter Capaldi, said at a Comic Con panel that he would never let a woman become the doctor, "not on his watch". I personally thought that the companions of Doctor Who had just as big of a part as the Doctor did, and the part suited well for females, Gilligan & Coleman, were actually my favorites, their attitude to not take things as serious as the Doctor did, was one of my favorite features about them.
But it also comes down to the fact that the BBC is trying to become as PG as it can, giving into SJWs left, right and center and agreeing with feminists over stupid ideas. I don't doubt that Moffat left the production team because he was constrained by the BBC, as we can see that the BBC are just shifting into an equal tomorrow, but sadly i don't think they'll ever learn that everything will never be equal in this world.
Your best bet is to get started right now...