I wasn't planning on getting her something Japanese I was just attempting to (and failing to) get across that it would be silly to get her something Japanese.

I was thinking of maybe a plant or an attempt at some cakes. Do these sound like good gift ideas? I also think I should include a thank you letter with the gift, written in the best Japanese I can manage (it'd probably turn out to be an embarrassing mess but that doesn't really bother me).

A pot plant doesn't sound a half-bad idea. It's kind of neutral and unlike cut flowers, doesn't have any romantic overtones. Maybe try and find a flowering plant that won't grow too big and isn't too high maintenance. It's too late for bulbs unfortunately, which is a shame as they're great gifts as you can normally bung them in the garden when they've finished flowering and they'll pop up again next spring, luck holding.

The most common "gift" for the teacher from the student is 寄せ書き（よせがき） if you want to know. Each student writing a card or letter separately is nice but we usually go for this in Japan. Each student writes a small message on it. It's also easy for the teacher to keep.

In Japan, it's not common to give teachers gifts of monetary value unless:

1. The teacher is retiring or
2. The teacher is relocating long-distance.

Then again, this isn't in Japan so you could add a plant or cakes as you said.
Just remember that if you are doing the 寄せ書き or an individually-written letter, make sure to present it the way that that is the main gift, not the other thing (plant or candies).

That would be great to do. However, there are some problems. I don't have contact with the other people in my class and the teacher will be in the classroom before I can see any of them to make one. I am going to a attempt a letter though. Let's hope it's readable. Thanks for the help everyone.

Also I went down to the garden center and the only gift size pot plants they had were cacti and venus fly traps. Cacti are lower maintenance so I chose one over the venus fly traps (also, maybe some people could be impartial to venus fly traps). It has a nice colorful pot at least.

That's great!! I hope your teacher likes it. And I hope I was of some help to you. LOL. :)