I'm unaware of any Disney location that does it, but I believe that there are a few surrounding Wal-Mart Super Centers. A lady I used to work with had just moved from Orlando, and I believe she said that they had 4? Not sure which one would be closest. At any rate, we pierce ears at Wal-Mart. Maybe not the Disney magical moment you were looking for, but if she wants it done ON her birthday, it may be an option.
I'd be hesitant to do it while I was down there, though. It will depend on how sensitive her ears are (i.e. whether or not they will get infected easily), and that's really hard to guage. My concern would be keeping them clean. Make sure you clean them immediately after getting out of the water if you go swimming. It may be easier to get germs and such on her ears being outside and at a theme park (sweating or just touching her ears without thinking about it). I know it may sound a bit paranoid, but I've seen some girls with some pretty infected ears, and it's no fun for anyone. Just make sure you clean them really well, which true enough, you'd be doing anyway.
I would suggest purchasing earrings for her birthday while down there, but actually get them pierced couple of weeks ahead of time so you know how her ears will react (in addtion to letting them heal a bit), or wait till you get back home.
I know that you didn't ask for a novel, but I've been piercing ears for close to a decade. I can't help it when I see ear piercing threads.
