I'm going to hang out with another girl and not tell my girlfriend
What is your reason for wanting to hang with another girl?
Because she's much prettier than my girlfriend.
You shouldn't be doing something like that behind your partners' back, even if the other girl is prettier.  When your girlfriend finds out you're keeping secrets like that she might break up with you!
I already told her, she just needs to get over it.
If you would rather hang out with another girl instead of your girlfriend than you are better off ending your relationship. All this is going to do is cause your girlfriend hurt, so if you do not really want to be with her than you should break it off.