I have done this a couple times. Disney is a great place for babies as long as you don't push them past their comfort level. I totally second slowing down and enjoying the day at a leisurely pace.
Here's a BIG Disney secret from a annual passholder: you are not going to see and do everything that the four magical parks have to offer on one vacation. I have been more than 10 times to Disney World on weeklong vacations, and I have not seen everything yet. So, accept that, decide what is important to you, and take everything else in a leisurely pace. You are on vacation afterall. You can come back and see more stuff when the baby is older. Couple of specifics:
-There are great Baby Centers that are each park. Find them on a map and plan your diaper changes around being close to one when possible. They have very nice areas for changing. Small potties for potty training toddlers, and peaceful rooms for nursing or bottle feeding. The baby centers are also quiet, have slightly dimmed lights in nursing area, and cool. They can be an oasis for a overheated, over stimulated baby with needs to get a clean diaper, cool off, and eat in a quiet environment. I find them soothing in a crowded park and wish they had an adult version. They also have baby supplies there in case you are one of the hundreds of people a day who lose their pacifer...or forget to re-stock the stroller with diapers.
Food: Portion sizes of meals at Disney are large and most kids meals at Disney come with yogurt and grapes or apples. We could easily feed the baby off the plate our plates (me, my husband, and older daughter) without buying an entire meal for them. My other secret on food is to schedule on sit down meal a day and make an advanced reservation online. It is nice to walk out of a bright/hot/crowded park into a nice table in a cool room. Don't worry about taking a baby to any place inside a Disney park. They all have kid's menus.
Entertaining: The most entertaining thing at Disney for a toddler is the Electric Light Parade. Make sure you get a good place to see this one. My toddler completely went nuts the first time she saw this parade because Tinker Bell blew her a kiss. My favorite is to push the stroller right up to the rope in Frontierland near Pecos Bill's outside seating area. The parade ends near here and it is less crowded than around the castle. Another good spot is in the Liberty Square area.
Stroller: I would invest in a very lightweight stroller with folds easily, but can recline. The Combi Flare Lightweight Stroller has been our favorite. It is lighter than an umbrella stroller, but very confortable. You will be lifting the stroller a lot. Everytime you get on and off the parking lot tram, you will need to take the child out, fold it, and lift it on the tram. This can be very taxing if it is heavy or if you over pack the stroller so that it is difficult to fold. Also, before you get to disney, buy a spray bottle of water that have a fan on it. You can get these for half the price at Wal-mart and kids adore them on hot days. The cool things about strollers at Disney is that you can safely park them in stroller parking outside the attractions and not really worry about them. I wouldn't leave anything of huge value there, but the only thing I have ever had stolen as a plastic poncho...I guess they really needed it.
Stroller Poncho: If you take a stroller, do not go without a stroller poncho. You can get these at Babies R Us. This will keep a sleeping toddler dry and the seat to the stroller dry during one of the daily showers that replenish Orlando. Showers come up fast in Orlando. I have walked in an attraction under blue skies and walked out into a rain storm. Luckily, I left the stroller poncho installed whether there was a cloud in the sky or not, so the stroller was not soaked.
Water Parks and Pools: Kids love the Disney Water parks. Both parks have kiddie areas for toddlers to splash in. There are a couple of family slides at each park that are safe for babies who are not afraid of water and swimming. Make sure you carry swim daipers to use any pool or water slide. Some Disney hotels offer splash pads at the pools for toddlers. My fav is at the Caribbean Beach Resort. It is a huge pirate ship that sprays water in the air every couple minutes.
*whew* I think that is all I have for now. Babies love it there. Both my kids really woke their imaginations while they were there. I really don't know how to describe it.