Giving any gifts - unless warranted for a justified reason - is Beta indeed. In most cases you should not even care it is her birthday. Unless you want to be friends with her, of course.
If you really like the girl and also honestly feel that she deserves you, then you might want to try this:
You have to get her friend onboard first, though (and be 100% sure she is with you on this)… unless you want to be eaten alive.