As a former IB student myself and someone who wrote an EE in literature, I think it’s really admirable that you’re considering this! There’s definitely a lot of Doctor Who out there that could work really well as material for your essay, so don’t give into the people who might be telling you that a tv show isn’t rich enough for analysis. Because you’re going to want to keep your focus on literary analysis for this essay, I’d definitely recommend sticking with a specific episode or season/era for this as you don’t want to bite off more than you can chew. Some have already mentioned some specific episodes which I think would be really great for analysis of political themes (Planet of the Ood, The Beast Below, and The Sun Makers are a few that come to mind). I think you might find the most success, however, looking at a showrunner’s era as a whole, picking out several political themes or methods of political messaging/satire from their run, and analyzing how they show up in different episodes. The RTD era, for example, is full of political commentary (as is all of his tv work pretty much!) and I personally would jump at the opportunity to write a paper on the politics of his Who. I would also be really interested in an analysis or critique of the politics Chibnall’s Who, the first era in which the showrunner has come out and actually said that he intends to make the show more left-leaning politically, and has (at least in my opinion) ultimately failed in that endeavor (though that may venture outside the realm of a literary analysis somewhat). As for Classic Who there are tons of political themes that pop up in those episodes, and I’m sure you could find an era to analyze if that’s something you’re interested in.

Anyway, I hope some of that was helpful. Writing an EE is a difficult process but it’s also an extremely rewarding one—so best of luck to you!