I've been watching my friend's cat, but I am going to make her take it back.
Why are you watching your friend's cat?
I do not like cats and I'm allergic to them. I'm just helping her out but I can't handle this cat.  Also, I prefer dogs.
If you are allergic to cats and you don't like cats, why would you agree to take care of her cat? You have to own up to your promise and man up. If you don't follow through with your promise it's going to look somewhat bad on your part and maybe taint the friendship.
I'm not a cat person and I didn't know it would be such a pain in the ass. She's only been my friend for a year and I'm giving this cat back.
If you can't fulfill your responsibility of taking care of the cat then by all means, get her to pick up her cat. However, you shouldn't make commitments and no follow through with them. You knew you didn't like cats and were allergic so you shouldn't have agreed to watch the cat in the first place.