I think it depends on your child, your comfort of having the child out in public, and how you view a disney trip.
We first took Holden when he was a little over three months old. But we weren't too concerned about seeing anything or doing anything in particular. We took him on some of the dark rides (I think only Pooh and Pan and Pirates), and watched spectro magic from the train station, which he loved. I have this great memory of him watching the parade, just entranced, and then that spot came when all the colored lights switch to white lights at the same instance and he just SPAT his passy out, he was so amazed. One thing is, his grandmother is in Florida and his Aunt comes down, so these aren't high pressure trips at all. We all stayed in a 2-bedroom villa at OKW and stayed a litlte over a week. We went to the pool, the living seas, that sort of thing. Just on our own schedule. Of course the washer and drier and dishwasher (bottles) helped a lot, and the big tub didn't hurt either. Yes, you do have to think about diapers, bottles, etc. We rented a car and trips to super walmart were made.
We took him again when he was 9 months or so. This was a family trip with about 25 or so people, and again, we weren't concerned about seeing anything in particular with him, and had lots of folks who wanted to spend time with him and hang out, and manage time with him. Again, Holden was on his own pace. He visited with characters and I have a really fond memory of him sitting on sleeping beauty's lap on a park bench at the international gateway. Chip and Dale held him. Or maybe that was the first trip, anyway, it was a lot of fun. We had 3 2-bedrooms for our group at the bcv, so the location helped. He really likes the living seas, I think this may be one of the best attractions for babies.
We went to mgm and saw playhouse disney and he had fun there.
Those first two trips we would only go to parks or something for less than 4 hours, fitting that around Holden's feeding schedule. That wasn't a hard and fast rule we came up with beforehand or anything, just what we realized we were doing. The baby care centers are great.
Direct flights are a good thing, but always over-prepare for the flight because you never know what will happen at the airport. Bring extra diapers, food in case of delays. Four months olds are easier on a plane than one year olds.
We just took him for a short trip a week ago, he turned one on Monday. We went to MK a couple of days and epcot one day, staying at wilderness lodge, again with grandmother and aunt. The lodge had a real crib, rather than the pack and plays of the villas. Again, we spent some time in the pool (He REALLY loved the bubbles in the quiet pool). Spent some time at the living seas, rode the boat in Mexico, looked at the lights. That was about it for Epcot. He had a blast. Over two days in an uncrowded magic kingdom, rode the jungle cruise, tiki birds, pirates, haunted mansion, pooh, peter pan, people mover, buzz, and country bears and the teacups. All are great with a one year old. He had a blast. Wow, he really, really loved Ohana, he was clapping and kicking his feet and laughing and really enjoying the singing. He also had a lot of fun seeing Micky, Minnie, Donald, Pooh, Tigger, and Eyore. They were so sweet and gave him time to play with them and stuff like that.
Now stop here and think about this for a second. Over two days, with little crowd in the park, we went on 10 attractions. Most of those are "secondary" attractions or fast loaders. Four were with a fast pass, the others were walk ons. Now, will you have fun going to magic kingdom with your baby and doing those things? We had a blast, the baby had a blast. In one very uncrowded day at epcot, we ate, rode on the Mexico boat, went to living seas. Would that be a fun day at epcot for you? (It was a blast for us). Throw in some pool time and some characters and you have a heck of a day (I would arrange character meals or things where you don't have to wait in line). Now this was with a one-year-old, we did less with a three-month old of course. What I'm trying to say is, if you view the time as fun time with your baby you will have all the fun in the world. If you are planning to spend most of your time riding splash mountain and tower of terror, or rushing to keep on some schedule or something, then I'd skip bringing the baby.
That said, Holden is a comfortable, secure, happy kid. I think that goes in to the mix and if he was fussier it might not be as fun.
I think dvc makes a difference in that you have more room and comfort. I think having family around makes a difference. For us it is basically just a family visiting trip. Poor Holden will probably grow up thinking his grandmother lives in walt disney world.
I think it would be a mistake to bring a baby if the adults are concerned about seeing anything in particular or have their own wishes about what they want to see for themselves. I don't think in three trips Melissa and I have ever "Baby swapped," where we stood in line with the baby and at the end took turns riding. But there have certainly been times when Holden was with grandma or something and we rode a couple of big rides. I remember one morning we went to MGM and rode the big 2 and the rest of the family met us a couple of hours later for lunch. But my point is, if the trip is really for older kids or the adults, then the baby isn't going to have as much fun, I don't think. But if you think of it as fun time with your family and just sort of taking the baby to the park for a few hours I think it is a lot of fun and the kids get a lot out of it. I mean it isn't really different from going to the park at home or to the mall or something or visiting grandma if you don't make a big deal out of it. Heck, I think with winter coats here in Michigan it is probably more difficult to get to the mall from home than to magic kingdom from the wilderness lodge.
I honestly think that there are a lot of stimulating things going on that helps their development. But that is being baby-centered in the approach. We just go for fun. Will he remember anything in particular? No, but he had a great time during the moment, and he'll see pictures/video and remember those. And we are kind of "disney people," in that we know we'll go again, we have dvc points, we'll bring him again, might as well get him going now. It is just what our family does. When he is four he can look back at those pictures and videos before he goes down there.
But again, we aren't concerned about agendas or seeing anything or "getting our money's worth," and those are very legitimate concerns, so if you have those things in mind, I probably wouldn't go with a baby.
This is all just my opinion and your milage may vary.