It really depends on your child. My kids were sleeping through the night at 6 and 9 weeks respectively and were very even tempered. I have a gf who has a colicky baby and I wouldn't attempt it with a child that is easily over stimulated.
We took our dd when she'd just turned 4 mo old and it was great. We just took it kind of easy, brought our own stroller that toally reclined and tha helped a ton. We also took the baby bjorn and stuck it under the stroller when she was sleeping, and I put her in the baby bjorn to carry her on the attractions. One of the beauties of Disney is you can do almost everything while holding an infant! The golden age of travel for babies is from about 3 mo when the colic stage is passed until they start walking. My philosopy is this: whatever kind of family you want to be- be that way from the beginning. If you are going to be an on-the-go family, go for it and take the baby, s/he will learn to adapt that way. Of course you have to make concessions for children, obviously, but we always traveled with our little ones, ate out with them, took them everywhere family oriented that we went.
We also got some adorable pics of our DD with characters, and the characters seemed to really like that, they are very adept at holding small infants- they get down on the ground and hold them in thier laps so you can take photos. It was priceless. Our dd LOVED it, she was fascinated by all the sights and sounds, and just napped in her stroller whenever she needed to. It was a great trip.
Have a wonderful time!