I was ALMOST 3 my first trip to WDW.
At that time only the Magic Kingdom was open, but I will tell you what I can remember (YES, I can still remember).
Small World-- I forced my parents on it over and over and over again.
Peter Pan-- My mom pointed out where the track "ended" and I was certain we truly were flying over London. Do not miss this ride for the world. Make sure she knows the story first! I'm sure she does already.
Dumbo- that's a no-brainer
Teacups-- loved this one too! Can't do it now though. *turns green*
Topiaries- simple but they managed to grab my attention, once my mom pointed them out to me.
Characters-- I wasn't afraid of the "big head" characters but the "real people" ones scared me to pieces. Poor Alice tried so hard. And I screamed in her face. I atill am not sure why. Maybe Stranger Danger.
The monorail-- No need to elaborate on this one!
Unless she is really, really brave I would skip Haunted Mansion and probably Pirates as well. I would imagine Pooh would be a HUGE hit with your daughter, as well as the Tiki Birds. Cinderella's castle will leave her spellbound.
As for the other parks-- Epcot does not have a whole lot to captivate a 3 year old, other than some really fun fountains and a couple of friendly parrots near Mexico. If she's like a lot of other kids she will probably like Animal Kingdom. You can get fairly close to the animals there. Plus there is Dinosaur Land, Camp Minnie Mickey, and, most importantly, McDonalds! MGM has a lot to offer little kids. I agree with Little mermaid, Playhouse, and the Muppets. Also if the Honey I Shrunk the Kids playground is still there (sorry, it's been awhile!) that is a lot of fun.