Me and my girlfriend were thinking of moving out and she went behind my back and now is moving in?

If it were me, I'd be sitting her down and asking her what her deal was and figure out why she decided to move in with other people... You may be reading into it? I guess if you consider it from all views, is her current living situation bad?
I think your first step if you want to continue this relationship with her is sit her down and just talk to her about it... Be honest and tell her how you feel & get her side. Depending on the result of that conversation you'll have to decide weather you want to deal with her response or tell her to kick rocks and forget about it... Hopefully that helps!