I teach a young preschool class (older 3s and 4s), and we've been talking about their vacations and where I'm going for vacation, etc. So here's my ideas, along with what they were most excited about.
As most have said, and I'm sure it's obvious to you as well, you can't beat everything the Magic Kingdom has for youngsters. From living the stories, to the parades, and characters, it is the one stop for the younger crowd.
My second would be Animal Kingdom. There are characters and animals, that's a one-two knock out right there. And if your child has a favorite animal they love to act like, a lot of the boys in my class are currently in love with lions, now they'll get to see them up close. And besides the obvious animal appeal of Lions and Tigers and Giraffes, and other creatures they already know, there are animals they might not know, or have ever seen. As well, I, as most do, don't think that Animal Kingdom lends itself to a full day yet, so you won't feel bad if you take a break in the early afternoon hours.
Lastly, as much as I am shocking myself in leaving Epcot out of a trip recommendation, I say you take the tike to MGM. To be brief, if your child has any experience with Playhouse Disney and the characters in that vein, this is the place to be. Not to mention, I feel that MGM has a lot of shady areas that are always helpful when trying to keep the little ones out of the sun.
Places to be, people to see:
Magic Kingdom:
Fantasyland
Mickey's Toontown Fair for characters (Mickey and Princesses)
Animal Kingdom:
Affection Section at Rafiki's Planet watch to get up close and personal with some critters
Camp Minnie-Mickey for some shows and characters
The Boneyard in DinoLand USA for playground fun
Kid Discovery Zones - one in each area, they have fun little crafts your little one might enjoy
MGM:
Playhouse Disney Live
Voyage of the Little Mermaid
Beauty and the Beast
I hope this helps in some small way, and I hope you have an absolutely magical trip!