I don't want my girlfriend to have a queer friend.
Why would you not want your girlfriend to have a queer friend?
I just don't want one hanging out with my girlfriend.
Regardless of how you feel your girlfriend has the right to be friends with whoever she chooses. Don't try to tell her who she can be friends with.
So I have to just suck it up and let it happen?
Yes, you don't control who she hangs out with. If you have a problem with queer people, you should find out way and try and change your prejudices.