Of the thousands of alternate dimensions in the TV Universe, there is at least one which is an Earth dominated by women. The 'Sliders' visited it in one episode (where we learned that the Pope was not John Paul, but Jane Pauley), and it even had its own TV series back in the 1970s - the Norman Lear serial 'All That Glitters'.
In this brave new Toobworld, such a gender reversal would affect even 'Doctor Who'. The main character would be a Gallifreyan woman (Time Lady or still a Time Lord, either way) and most of her Companions would be handsome young men*.
If they all followed the templates laid down by the originals in Earth Prime-Time, then the Eleventh Incarnation of the Lady Doctor would look something like this:
(That's Erinn Hayes from 'Children's Hospital'.....)
* If the male Companions are gender-switched versions of the originals, there's one who wouldn't have to go through a name change - Mel Bush.......