I hope you don't mind that I point you in the direction of a few great choices, and let you make the final decision depending upon your exact preferences.
There are lots of great "adult" dining choices.
Brown Derby,
Le Cellier, and
Artist Point come immediately to mind, but these
might not be that special for your daughter. If your daughter isn't ready for, or wouldn't enjoy an "adult" meal, I'd skip these options.
If you are in the mood to be a bit silly on your B-Day, then I'd recommend a character meal at either
Chef Mickey's or the
Crystal Palace. This could make for a great mother-daughter experience as you all enjoy some quality time and photos with Disney's characters.
If you are in the mood to be treated like a Princess, then
Cinderella's Royal Table would be perfect for you and your daughter. If you choose this option, I'd recommend breakfast or lunch, as the princesses are only scheduled for those meals.
One last idea that might be fun:
50's Prime Time Cafe. If you get a good server, I'm sure they could involve all of the table in the fun. Wouldn't your daughter love to see mom getting in trouble for not eating her peas?! ;-)
Have a splendid trip!