The resort stores do carry baby supplies (not a lot, but they do have them). If you are staying at a resort that is also a vacation club property the selection is a little better (Wilderness Lodge, Yacht and Beach Club, Boardwalk, Old Key West, Saratoga Springs). If you don't want to go to the grocery store (as suggested by the other poster) you could also go to Downtown Disney and walk across the street to the Hess gas station, while not a huge offering, they have more than the resorts do).
As far as the parks go, each park has a Baby care center which is nice to go to to relax for a little while with them. Here is the info on those locations (where they are located and what they offer):
Animal Kingdom- Located behind Creature Comforts in Discover Island.
MGM- Guest Services Building
Epcot-Next to the Odyssey Center and Epcot First Aid
Magic Kingdom-Behind Casey's Corner on Main Street
Baby Care services are facilities for guests to feed, change and nurse their children. There are highchairs, nursing rooms, changing tables, and a microwave to heat bottles and food. Guests can also purchase formula (no milk), bottles, and pacifiers, cold and allergy medications and children's undergarments, t-shirts and baseball caps. Baby Care Centers are also the central locations for lost children. No babysitting services available.
Hours: park open until park close except Epcot whose hours are 8:30am-9pm