Hi Christina!
Thank you for sending in your question to the Walt Disney World Moms Panel!
You definitely want to visit the Magic Kingdom. It is the crown jewel of the Walt Disney World Resort and, in my opinion, of the entire theme park industry. Chef Mickey's for dinner sounds great. You just need to hop on the monorail from the Magic Kingdom to the Contemporary Resort. After dinner, you can take the monorail back to the Magic Kingdom.
While you are in the Magic Kingdom, you might consider visiting the
Bibbidi Bobbidi Boutique. There Fairy Godmothers'-in-training can transform your daughter into a little princess. It is relatively expensive but everybody I have talked to who has done it for a child said it is absolutely worth every penny!
For your second day, I think Disney's Animal Kingdom is fine. If you go there, I suggest going to Tusker House for lunch. It is a lot of fun and the food is fabulous. However, you might also considering going to Disney's Hollywood Studios which has a lot of attractions, especially shows, suitable for a young child. In fact, if money is not an issue, you might consider going to Disney's Hollywood Studios in the morning and then park hopping over to Disney's Animal Kingdom in the afternoon.
If you go to Disney's Hollywood Studios, be sure to visit Toy Story Midway Mania first thing in the morning. It is a fantastic experience for the whole family. Also be sure to see Fantasmic! Fantasmic is my favorite nighttime spectacular in all of Walt Disney World.
I hope this helps! Please write back with more questions!