So im dating this girl that lives in LA and she doesnt want to make it serious till i move there.?

She still wants to sleep with other guys though until then. She doesn't think of sex as that important of a thing like i do. I told her that if she does then not to tell me about because i think i would get jealous and upset if i knew. Should i just put up with it for now till i move down there? I really like this girl and would definitely like to have a relationship with her eventually but is it worth getting depressed over or my sanity? Help me out here...