We took DD at 2 mos and she was a breeze. We just took her again in July at 8 mos and she was even easier. At 2 mos, they sleep all the time. It is more time consuming to go w/ a little one, but as long as you're in the mind set that you are going to take an afternoon break I think you'll be fine. DD got over-stimulated on our first trip (no afternoon breaks) and so we learned for trip number 2. We had such a great time.
The only thing I would think about is if you're planning to breastfeed or formula feed. I breastfed so if DD was really hungry and we weren't close to a baby care center, I could just find a place to sit and feed her. I can't imagine trying to formula feed, finding water, mixing, measuring, warming, etc. It seems like a big pain to me. Nursing is so easy. Diapers are really no big deal at all either, don't let people scare you away!
I have a pre-trip report from our first trip w/ DD at 2 mos that I pm-d to another diser when we got back. If you'd like it, just pm me, I'd be happy to send it to you!
Ps. I don't get why everyone focuses on "we'd rather go when they can remember it." My parents took us when I was 14 and my sister was 5. My sister who is now 17 doesn't remember that trip. Who cares if they remember it at 2 mos? You will. You'll have priceless pictures and memories. Not to mention, it won't be like you wasted money, they are free!
I will say though, DD definitely enjoyed the trip we took when she was 8 mos. We took her on almost all the rides and she really enjoyed the colors and lights and she especially enjoyed the characters!
DD loving Donald and touching his beak.
DD terrified of Mickey at 2 mos. This picture alone was worth the trip, it will always make us smile. She was perfectly fine w/ every other character that morning, just not Mickey, lol.