I plan to break up with a girl after we have sex.
Why would you want to have sex with her before breaking up?
The question is: why wouldn't I have sex with her?
It's generally inappropriate to have sex with someone you're planning on breaking up with. If you only want to have sex just make sure she understands this and she doesn't assume that you want to have a long term relationship.
It's not like we're in love or anything.
That may be true, but just make sure you are both on the same page. Breaking up with her after having sex could be emotionally painful for her if she thinks you two are going to have a relationship.