if you're dating, you're more than likely feeling the chemistry out to know if she's someone you want to spend "more" time with. and by more, i mean a helluva lot of time. so the thing to consider is.. is the chemistry just not working?
your girlfriend is someone you want to become your best friend. if you aren't having a good time, what's the point? now i know that you *might* be having a good time despite the silence, which is actually healthy. but i'm not getting that vibe from you. it sounds like awkward silence.
i'm not saying to jump ship, but be honest with yourself about how well it's working out. and establish something in terms of where you two are at. i mean, let her know your intentions, at least. that does a lot for a relationship.