Hi, Amanda!
Well, you have a couple of options for your little princess's big celebration, so I suggest that you follow the first suggestion below as Plan A, then keep trying for Plan B, too.
Have you considered booking an appointment at
Bibbidi Bobbidi Boutique in Downtown Disney? There might be an opening at that location on the day you'd like to celebrate your daughter's birthday, and she'll be thrilled at the attention the Fairy Godmothers-in-training will shower upon her. Next, perhaps a lunch or early dinner at
Akershus Royal Banquet Hall in Epcot's Norway Pavilion would be a wonderful way to commemorate such a very special day. We often select this option over Cinderella's Royal Table, for a variety of reasons, and have never once been disappointed with our choice. You'll still be able to dine like royalty, while Snow White, Cinderella, Belle, Princess Aurora, Ariel and Mary Poppins mix and mingle with Guests, and your daughter will feel like a real princess as you dine in this beautiful space.
Plan B includes calling (or going online) each day from now until the big day, hoping to catch a cancellation. Guests change plans every day, Amanda, so what may not have been available previously may suddenly become available, especially as the date gets closer and plans are finalized.
I suggest securing your Plan A reservations, then, if you really have your heart set on BBB in Magic Kingdom and dining at Cinderella's Royal Table, keep calling back in the hopes of catching one of those cancellations. You can always cancel your backup plan, should you manage to get the other reservations in the end.
Send another question for more suggestions, Amanda; there are lots of similar ways to celebrate at WDW, and I'd be happy to share them with you!