I would agree that CP would be a delightful place to spend your birthday, but just a word of caution: When we took my then 2 year old DD to CP 4 years ago, Piglet came by first and she was thrilled, but then Tigger came by and she absolutely freaked out. After that, she would have nothing to do with Pooh and Eeorye.
If you have any inkling that your DD may not like the characters (and we didn't), you may want to consider going to CRT, or maybe 1900 Park Faire. I've never been to either but I think all the characters have faces, if you know what I mean.