When my kids were that young, we could take them on all slow moving dark rides because they didn't get scared (i.e. haunted house, snow white, etc.).
My kids are 5 & 2 and they still go on all those rides. Since we went on them often (AP at DL), they got used to them. However, my dd5 won't go on Peter Pan. Maybe it's because you're above the action looking down. I think that the boats have a feeling that you could fall out easily.
My #1 favorite place with a baby at WDW --- Hall of Presidents! It has ac in the summer and heating in the winter. The show last about 20 minutes and it is dark. My kids have fallen asleep in there everytime!!
A lot of the rides at Epcot used to be slow going rides, but they've taken a lot of them out and replaced them with fast rides. Try Spaceship Earth, Living with the Land (boat ride), Crush at Living Seas (kids love the aquarium too), Maelstrom at Norway (one dip), Rio del Tiempo at Mexico (my kids LOVE this ride and usually we go multiple times in a row). Walking around the countries is fun and a baby can veg out in the stroller.
The above suggestions are great and rest assured, there is plenty of things for you to do with a baby.
One other suggestion.... take advantage of the baby centers. The centers at MK and AK are great! They are airconditioned in the summer and heated in the winter, they have nursing sections, changing tables, private potties, high chairs to feed your little ones, microwaves to heat up their food, and at AK, they have a play area with a video running.
Enjoy your trip!!