I would say there are no prerequisites at all!
Abstract algebra is one one hand a very self-contained subject. Everything can be defined abstractly, and you can prove interesting theorems without knowledge of anything else in mathematics. Knowing little bits of classical algebra, linear algebra, number theory and even calculus can help you to see some applications of what you learn, but studying the concepts by themselves does not require these things.
Something really nice about algebra is that you can study it in itself, but it also touches on nearly everything else in math in some way or another. Linear algebra is the prime example, but groups, rings and fields (the central objects of study in basic abstract algebra) are also really common in other areas. When you eventually go on to study other more specific topics, you will find these things crop up again and again, so it will be good to have seen them at least once before.
I don't know about the book that you'd be using, but in my experience, algebra is a fine place to start studying and proving theorems. In group theory, especially finite group theory, the basic theorems are all quite natural and accessible. As you delve into it, the material gets harder at a slow but steady rate, and the techniques and tricks used in the proofs also get more complicated. This is a good thing. It helps to broaden your mind and increase your sophistication.
As always, if you get stuck, don't be afraid to talk to your instructor, or ask here. I'm sure they'll be able to help you out. I'd like to throw out a few books that are good for studying algebra while you're at it, in order of my preference for them when I was at your stage.
1) Galian - Contemporary Abstract Algebra. Friendly. Concise, including only what you need to know for a first course. Basically everything you could want in a first book. At the end it has a bunch of interesting topics that you probably won't see in a first year course that are really cool to touch upon, since they are not any more advanced, just a little more niche.
2) Aluffi - Chapter 0. Has a completely heterodox viewpoint on algebra. Works from the categorical perspective. If you've not seen anything to do with categories before, this is probably harder. Nevertheless, the book is certainly a warm introduction to algebra and does not assume the reader knows any algebra.
3) Dummit & Foote - Abstract Algebra. I used this to study group theory on my own, and it contains lots of little gems in algebra. While it does not assume the reader knows any algebra, it is a massive book, and can be a little intimidating. The style is sometimes a little more terse. All in all though, persistence can be really rewarding. This book inspired my first "love" in mathematics in ring theory (specifically polynomial rings), and convinced me to do an independent study in polynomials of several variables and Grobner bases.