There are tons of attractions for that age!
Mk:
Jungle Cruise
Tiki Lounge
HM (at that age they don't know enough to be scared)
Pirates of the C ( we took our baby and she was never bothered, but there is a noisy shooting sequence)
Small World
Peter Pan
Mickeys Philharmagic (it's 3-d and your babe may not keep her glasses on but babies can still go)
Snow Whites Scary Adventures (there is nothing scary about it for baby)
Pooh's honey pots ( i'm not sure of the name, but it's the winnie the pooh ride)
Baby can see all the parades and fireworks and Cinderellabration on the Castle stage. Baby can also meet the characters at toon town fair. I believe there are no height restrictions for Barn Stormer, Dumbo and Alladdinn.
MGM:
Beauty and the Beast show
Playhouse Disney
The little Mermaid Show
Great Movie Ride ( there is a noisy shooting sequence during the western part, so if your baby is jarred by noises, stay away)
Muppet Vision 3-D ( Baby probably won't wear the glasses for long, but it shouldn't keep you guys from enjoying the show).
Fantasmic ( it has some intense scenes, but babies don't know what to be scared of. I've seen many babies at fantasmic, mine included)
The afternoon parade
Epcot
Character Connection (a great place to meet the characters, rarely crowded).
Turtle talk with Crush
The Land
Spaceship Earth ( long and completely relaxing)
Journey into Imagination with figment
El Rio Del Tiempo
Maelstrom
There are many shows in the World Showcase that you all will love such as American Adventure Show, The acrobats in China, There is a rock group in Canada called off kilter, that everyone seems to love, the drummers in Japan. Just get show times.
She can also do some scribbling at some of the kidcot funstops. There are also many characters around World Showcase.
AK
Pocahontas's Show
Festival of the Lion King
Affection Section ( it's a petting zoo)
Wild Life Express Train
Triceratop Spin
Kilimanjaro Safari
Flights of Wonder (it's a neat bird show)
The afternoon parade will be fun for baby. Just wandering around seeing all of the animals is a thrill for babies.