I can't tell you what to do, but assuming you care for her a lot, some arguments for staying with her would be:
1. Even adults make mistakes
2. You believe her that she feels horrible about it, the fact that she didn't try to hide it is probably a good sign
3. No relationship is perfect, and if this is a one time thing it isn't really a big deal in the scheme of the 60ish years you might spend together if you think you're going to stay together
4. Say you break up and date someone else, and that someone else cheated on a previous boyfriend. Would you never date someone who cheated on someone ever (and how would you know)? If some guy dates her and hears she cheated on a previous boyfriend, would you expect him to dump her immediately? In other words: Would you rather forgive your girlfriend for cheating on you, or have someone else forgive her and live the rest of their lives together?
I was in a similar position at one point when I was young, and things ended ok. I broke up with her eventually for different reasons. We dated for years, and we grew and moved past it eventually. I'm not really good at analyzing feelings or anything like that so I can't really give you advice.
For me it would really just depend how much you care for her and what future you think you'll have together.
(On the other hand maybe you don't care for her that much and you're just wondering if it's worth the hassle of moving your stuff out of the apartment -- in that case I don't have much advice except that you should probably hire movers, moving stuff on your own is a real pain and it's really just better to pay someone to do it for you)