My youngest was 5 weeks old when we took our last trip to WDW. We didn't intend to - but the vacation was planned before I knew I was pregnant, and I just couldn't see myself telling my older two that they couldn't go to Disney World because of their new baby sister.
In the end, it was, quite honestly, one of the best family vacations we've had!
We drove, which was nice, because we could take our own car to the parks and not have to worry about dragging a stroller and giant diaper bag on the buses. Sometimes one adult would take the baby and her gear, while the other one rode with the kids on the monorail or bus.
It was early December, so I wasn't worried about excessive heat or sun, and was able to carry the baby in a sling throughout the parks, occasionally putting her in the stroller when I wanted a break.
We stayed at AKL, and the room had plenty of space for all five of us, including the portable crib, which Disney supplied.
I don't remember if she was sleeping through the night yet - she might have been, but honestly, with three kids, I don't think I've had a completely uninterrupted sleep in a decade. Someone is always having a bad dream, or can't reach the bathroom light switch or something.
I will say, my daughter was an easy baby - she wasn't colicky, she would sleep and eat under any circumstances. She did cry every now and then, but was never inconsolable. With a less easygoing baby, the trip could have been a nightmare. And, I had an easy, uncomplicated delivery, so I felt fine myself, and was actually eager to walk around the parks and get some exercise.
However - we did have alternate plans in place if we felt that the baby wasn't up to the trip. Because we were driving, not flying, and because we weren't buying our park tickets until we got to Florida, it would have been no financial loss for the baby and I to stay home. Another possibility was my mom stepping in to take the baby for a week, while I went on the trip.
Good luck with whatever you decide.