I think you should go to the birthday girl first and greet her, even if she's talking to someone else at that moment. That's common, I think. She is the most important person and should know that you're there and have thought of her birthday. When this is done, you don't have to worry about talking to her anymore and can enjoy the party.
Do you bring a gift? Or is this not expected, because you don't really know her? If it's a private party (not at a bar/restaurant), you could also bring something to drink or eat. But I don't know exactly what is expected in your peer group, it's just what I and my friends would do.
By the way, this girl who will be there with you, it sounds like you won't have to worry that something could go wrong with her. ![Very Happy :D](./images/smilies/icon_biggrin.gif)