Generally what my school told us was that we couldn't write our EE in a subject the school didn't offer. Idk how others work but the general idea is that you have to learn the content before you can write your EE (or at least get a broad idea of it anyway). Doing that on top of your subjects is honestly just not worth it, especially for just one essay.
Also, apparently in psychology the marking for EE is really subjective, so if they don't like your topic or essay in general then they'll give you a bad mark (at least that's what I'm told).
Honestly, I wouldn't go for it. It's risky, and if you have to learn content for a whole other subject too then I wouldn't do it.
I'm not saying you couldn't do it, but you don't have a huge amount of time for this essay and your other subjects do eat your time up very quickly, so to save yourself stress I probably wouldn't.
In any case, good luck with your EE, I hope it goes well whatever you choose!