You need to ask her if it's exclusive yet or not.
I've been 'seeing' a girl for a few weeks now, but it's not that serious yet. I'm going travelling soon, is it acceptable to sleep with other women whilst I'm away? Or would this be considered cheating?
I would personally consider this cheating — if you're not sleeping with other girls while you're at home because that's cheating, why should it be any different when you're travelling?
You don't sound too serious about the girl you're currently seeing — I understand you haven't been together long, but if you're thinking of sleeping with other people when you're away, it doesn't seem like you're that crazy about her.
Either way, this girl won't be happy with you sleeping around when you're travelling. I think it's probably fairer to break up with her before you go, if you do want to sleep with other people when you're gone. If she finds out about it later on in the relationship, she'll be upset, and you probably won't want to deal with her anger, either!

If you don't want to end things with this girl, don't sleep with anybody else, either. Alternatively, compromise and take her with you — it could be a good chance to get to know each other, too!
