Hi Natalie!!!
Congratulations on planning your Walt Disney World Vacation for your daughter's 2nd Birthday! I just recently got to spend my son's 4th Birthday at Walt Disney World and it was so much fun!!!
There are two Character Dining Restaurants that I would recommend for you to book for your family. The first is
Chef Mickey's at Disney's Contemporary Resort. This restaurant offers breakfast and dinner buffets with Mickey Mouse, Minnie Mouse, Donald Duck, Goofy, and Pluto! There is a huge variety of food options for all ages and your daughter will get some wonderful time with the Fab Five!!!
Another restaurant that our son loves is
The Garden Grill at Epcot. A family style dinner is served with Mickey Mouse, Chip, Dale, and Pluto in a very unique rotating restaurant around the Living with the Land Attraction. It is so much fun when Chip and Dale are close by and start interacting with each other and with the children in the restaurant!!
I definitely think your entire family will enjoy either or both of these Character Dining Experiences.
Please let me know if you have any other questions that I can assist with!!
Have a magical trip!!
Scott