I want to end things with a girl who doesn't want to have sex
Is that the reason you want to end things?
Yes it is. It is annoying me.
Her not wanting to have sex shouldn't be a deal breaker and you should respect her wishes. Ultimately though, if you are not getting what you want out of the relationship, then it is probably best to end things and move on.
But I think she is really cute.
Regardless of how she looks, it comes down to what each of you want out of your relationship. If sex is something you feel you need with a partner then it's appropriate that you break up.