We took my son for his 1st birthday and found there's quite a lot they can go on:
Disneyland Park: Buzz, Small World, Storybook Boats, Casey Train, Dumbo, Tea Cups, Carousel, Pinocchio, Snow White, Peter Pan, Phantom Manor, Pirates of the Caribbean.
Studios: Cars (but hold onto them tight!!!), Slinky Dog, Magic Carpets.
There's then the shows. My son loved Playhouse Disney and Animagique. He sat through Cinemagique but wasn't interested and was scared of the stunt show!
There's lots they can do, how much they enjoy it is another matter. Some of the rides are very dark and that upsets some kids. My son seemed to just like the colourful ones and the ones with catchy music. Small world was a big favourite with him and he'd wave goodbye to the characters at the end. He also loved the tea cups. On most of the other rides he just looked a bit puzzled.