Ehhhh...
I'm not into the idea of posting on her wall wishing her a "happy birthday". I don't know her. It would just seem awkward to me.
Bring her here to see this question so that she can see me wish her a happy birthday here.
Yeah because having a total stranger who she haven't met before her entire life greet her a happy birthday will cheer her up and not mark you as a creepy stalker.