Hi, I am also on a gap year so I understand, to a good extent, how you feel.
I think the main problem here is how you view a gap year should be. For instance, I went on my gap year not exactly by choice, and I felt so "behind" and lonely the whole time. To be honest (and maybe this is because of a cultural difference since I'm not from the UK), I didn't feel the need to travel in my gap year. There's never been a time when the word gap year = travelling for me. I had the fear that being in a gap year, I would be disadvantaged in my applications to uni later on so I made it a point to "add" to my skills and learning. I spent 90% of my gap year alone, working my internship and volunteering, but I was quite okay with that because I was working towards my own goal and paid no mind to what others thought of my journey (besides, my other classmates were more than busy with their own uni work to care about what I was doing). Of course, this is different for everyone.
Don't worry about not travelling during your gap year. You're not failing just because you're not meeting the aesthetics of a gap year. It really is such a privilege to travel that way and don't feel pressured to travel just for those 2 weeks just to make your gap year "aesthetic". I promise you it's not that big a deal once you actually get to uni. Everyone has their own journey and you don't need to follow a path others take just for the sake of taking it or because you're worried about how you're perceived. Just as you said, if you take a trip for 2 weeks, you wouldn't have anything else to do until May. Unless you can figure out how to fill that time (perhaps another job/internship/volunteering/etc), I think you should give it a real hard think again. Just do what makes sense to you with what you have, according to your own terms. As long as you're genuinely happy by the end of it, then that choice was worth it.