You will probably get more replies to this question on the Families board...
But anyway, we visited WDW with our 5month old last August. If you are going to use a stroller definitely bring your own, keeping in mind the busses/trams. There are really great umbrella strollers out there that recline, and have baskets and canopies, but they are expensive. Definitely bring a baby sling or soft carrier of some type because there are many places where strollers aren't permitted. My dd only used the stroller one afternoon during our trip...she hung out contentedly in the sling the rest of the time (and my 5yo used the stroller). And she slept a lot.
If you will be nursing this will be about the easiest WDW trip with the baby that you'll ever have....no concerns about feeding, just keep a stash of diapers with you and you're set. All the rest rooms have adequate changing facilities. I've heard great things about the Baby Care Centers in each park, but have never set foot in one. I really found no reason to use them...dd nursed in the sling whenever she needed to (and did most of her eating overnight at the hotel). But they sound nice to take advantage of if *you* need a break...rocking chairs, etc...
One big recommendation....do at least one character meal! I know it sounds funny but my baby just couldn't get enough of the characters...we had 2 character meals scheduled and added a third after seeing how much she enjoyed them. All the sights and sounds of WDW are great fun for babies too. One thing I would avoid, unless you don't mind taking turns eating, is making lots of PS's at the nicer restaurants. We did several of these too last trip and usually ended up trading our dd off and taking her outside to keep her from fussing in the dining room. Counter service was much easier, and even though we enjoyed our nicer meals, if I had to do it over again I'd do less sit down meals and keep them to noisier places.
Have fun!