Hi Jennifer!
There are so many things for a child under 2 to do! The first two times I took my kids to the parks, they were under 2!
Each park has several special spots that are just for little bitties--there are even playgrounds! My most favorite tool to help people (including myself) pick the right attractions for toddlers and infants is the
Magical Beginnings map. You can download it and print it now and plan what your baby will like. The highlighted attractions will be MUST sees for you and your toddler.
But my personal fave? It's a Small World at Magic Kingdom, Festival of the Lion King at Animal Kingdom, Playhouse Disney Show at Hollywood Studios and the Imagination! Pavilion in Epcot!
Also, don't forget about the Baby Care centers in each park--they have changing tables, high chairs, a TV and private nursing areas. It's a nice air-conditioned break when your kiddo needs it!