My thoughts:
The Doctor - Consistently ENTP and a probably a sx/sp 7
You could make a case for some incarnations as introverts but generally he's someone who needs a lot of outside stimulation, is very energetic and deals poorly with being on his own.
The Master - I concur with ENTJ, also sp 3.
Rose Tyler - ISFP sx7 (Think about it. It explains/ reconciles everything. She's very ideal-driven (see her speech to Jackie in "Parting of the Ways"), but doesn't really talk or reason like an intuitive. There's a subset of ISFPs that can be easily mistaken for extroverts, whn you think of it she has a few strong connections rather than numerous ones.)
Martha Jones - ISTJ Also very distinctly 2w3, her character journey is basically about learning to tell herself thst she's good enough and should learn to look after her own needs. She's also very loyal and has nerves of steel.
Donna Noble ESTJ; an 8 if there ever was one. The show does a good job at showing off her strenghts and letting us look inside her while still keeping her as a fairly typical one.
Amy Pond ESFP sx 7 (Those can be artsy, too! Her style in relationships and careers (tried out many on short notice before she felt reay to stick with one she really really liked) and decision making (at her worst, impulsive, at her best, has great wisdom and intelligence but it's the "gut feeling" sort rather than resulting from elaborate reflections) all point in that direction. Yes, she was bullied as a kid but that doesn't immediately make her an introvert, she's kind of a "peach" (easily and confidently approaches new people, but ha a core of inner feelings she's a bit more reluctant to bare) than a coconut (hard shell soft center) when it comes to opening up. )
Rory Williams ISFJ, phobic 6 (Starts out timid yet sceptical, gradually becomes loyal and valiant, loyal af, works as a nurse, his biggest dream is to be a father and peacefully live with his wife.)
River Song - ESTP 8w7 (Her younger self is rather wild and impulsive, but we see this character grow alot and becomes quite caring and wise and show all the strenghts.)
Clara Oswald ENTJ 8 (Though you'd be forgiven for classifying her as an F as she really wears a facade, especially early on in series 7, "Role Function" is a good concept to keep in mind here, her real self is actually somewhat awkward when she isn't using her artificial charme, see when she keeps inadvertedly offending Danny or the clumsy jokes at her family christmas Dinner... Her real self (which we get a good glimpse of as early as "Hide") is actualy this very articulate, dignifiedly-assertive person who actually relishes danger and responsibility and can sometimes be ruthless. She has the control issues 8's sometimes have but also the protectiveness of others; It's just that you mostly see the latter at first. )