As the title says. I imagine this game is perfect for one-on-one games (1 GM, 1 player), but I wanted to make sure before I tried playing it that way. Would a GM-run companion be required or would it be fine for the player to just be the Doctor/Time Lord/other character by themselves? Also, are there any premade adventures that would be well-suited to this playstyle? (Bonus points if they’re good beginner adventures)
Hmmm. I haven't tried one-on-one with AITAS. IIRR some of the Diary scenarios/articles covered it. Personally I'd have an NPC accompanying the solo PC, if only for the get-out-of-nail situations. It could be a Time Lord, Time Agent or other ephemeral.
As for a starting adventure the published scenario Stormrise seems like a good option. I've used a modified version. I can post more details if you like.
Time, time,time, see what’s become of me. While I looked around for my possibilities... My AITAS files.
Well it works extremely well; I've been running a one-on-one campaign for 10 years or so (we've played circa 200 episodes) - see the notes on Lady Penelope's Odyssey in the Campaign section (or my blog).
As for GM-played companions, it all depends on what your player wants! I'd say don't start with one and go with the flow. Over the course of her 13 seasons of play, Lady Penelope has had a very small number of NPC companions - and it worked equally well with or without one. And the departure of her first companion was a real heartbreak - she never really replaced him but from time to time took another passenger in her TARDIS for a few episodes or, more rarely, a longer period. But this always resulted from decisions made by the player during actual play - in fact, she just did this at the end of the scenario we've just finished playing!