Ignore the people who say you shouldn't bother with online relationships. They're ignorant of the subject. But just for the record, it does take a great investment of time and money, and you need to be willing and able to meet each other. Fly out if you have to. You need that connection.
As for being jealous... yeah, it's understandable. It's a tough situation. You shouldn't tell her no, because then you'll be a controlling jerk, but at the same time, cheating always starts from harmless conversation. You just have to decide if she's trustworthy or not and if not, perhaps you shouldn't be with her anyway. But if she is, let it go. It depends, really. Someone you stay up late talking to is probably somebody you like, and I'd be concerned about that. Better make sure you work through stuff like that before you take a relationship to the next step, though.