He's not any more bulletproof than anyone else, after all.
That's true.
Having thought about it some more, the issue comes down to the Doctor not really fitting the Dresden Files. The Dresden Files are a fairly hard magic system, and the game represents that pretty well. Creature X has Power Y. Power Y gives benefits Z. Doctor Who, by contrast, is sci-fi as soft as soft-serve ice cream on a warm day.
The best way to represent the Doctor, for me, is going to be entirely through aspects, which are the softer side of the Dresden Files. He'd be entirely at home in FATE Core, really. The Powers section of the DFRPG doesn't really fit, because powers in Doctor Who vary according to the demands of plot. On the other hand, that's exactly how aspects work too.
The Doctor is just a character with a lot of Fate points, some fairly well-rounded aspects, and a tendency to take every compel that comes his way. His toughness is just him Invoking his "Timelord Biology" to shrug off things that would kill regular people. He can Invoke his "Sonic Screwdriver" aspect to open doors, mess with computers, as a sensor, or as virtually anything else the player can think of (But it doesn't do wood). He'd be frequently compelled to get involved with the troubles of other people - I'd be tempted to use "old, and kind, and the very last of his kind" (The Beast Below) as the Eleventh Doctor's Trouble, for example. It basically sums up the beginning of season 5. The end of Season 5 and throughout Season 6, his trouble would reference the fact that he's got a lot of people against him. I'd be tempted to go with "And all this in fear of him", as a reference to River's speech in "A Good Man Goes to War".
This was exactly you. All this, all of it. You make them so afraid. When you began, all those years ago, sailing off to see the universe, did you ever think you'd become this? The man who can turn an army around at the mention of his name? Doctor? The word for healer and wise man, throughout the universe. We get that word from you, you know. But if you carry on the way you are, what might that word come to mean? To the people of the Gamma Forests, the word "Doctor" means mighty warrior. How far you've come. And now they've taken a child... the child of your
best friends... and they're going to turn her into a weapon, just to bring you down. And all this, my love...in fear of you.
Having said all of that, I realise that this isn't too useful if you're actually wanting him in your game. But I think it's still a good starting point. And if you're in a sufficiently low power game, giving him a good spread of aspects and a ton of Fate points wouldn't be a bad way to play him. If he's getting into combat, something has gone wrong (but in terms of Social conflicts, I'd watch out. He's fully capable of
breaking pretty much anyone By talking, and frequently concedes physical conflicts in order to give him the opportunity), so quibbling over whether he has Inhuman Recovery or Inhuman Toughness is probably not too necessary.