My daughter is 17 months now and has already been to Disney a few times. There are a lot of rides at the Magic Kingdom that are baby friendly, like Winnie the Pooh, the Little Mermaid, Peter Pan, Dumbo, Jungle Cruise, etc. The Enchanted Tales with Belle would also be great, as well as the character meets. Mickey Mouse in Town Square Theater is fun because he actually talks to the kids! We stayed at the Wilderness Lodge the first time we took her, and it was VERY convenient being able to take the boat right from the resort to the entrance to Magic Kingdom. We didn't have to fold up the stroller for the boat ride, and it was a quick ride to the resort for a nap.
The family suites at Art of Animation would be a good choice too because the baby can sleep in one room, while you can stay up in the other without disturbing her.
While it's true that she won't remember the trip, we've always enjoyed going and the pictures and memories are priceless.