Honestly, it just sounds like she's flaky.
When you said she played you, I initially assumed you meant she cheated on you when you were getting into the swing of dating each other. My sister went through that, after HE told her he wanted to be exclusive, but somehow thought that meant he was free to date around when she was away on a trip.

THAT was being played! She put down some ground rules after a serious discussion with him and she's still with the guy.
That doesn't sound like what happened to you. She owes you nothing at this point and you owe her nothing. You even call it "hanging out," FFS. Either let it go and keep it cool about the flakiness until the relationship is more serious, or if you don't like flaky people, move on.
It's really up to you. My sister and her aforementioned bf moved in pretty quickly after getting exclusive and they have personality clashes at times, but it's never really about boundaries. It was the first time she's ever moved in with a guy. And the personality clashes would probably still exist if they waited too.
The most important thing IMO is to keep communication very very open. Although if you're feeling hesitant, it's probably best to wait.
And just because you've talked about it, doesn't mean you have to do it right now. My bf and I talked about how we'd feel comfortable moving in together pretty early on, but it didn't happen until like, a year later.