Hi Susan,
Thanks for visiting the Moms Panel, you've come to the right place for advice on vacationing with little ones! I know it can seem like a lot of work to bring such young children to Walt Disney World, but from my experience these have been the best family vacations!
Each of the Walt Disney World Resorts offer a store that offers a limited selection of groceries and sundries. Depending on where you stay, the resorts may have larger selections (such as at the Vacation Club Resorts). The items tend to be a bit more costly than you are probably used to paying, but the convenience is what makes it an attractive option.
One of the things that I have always done when traveling with babies is to ship myself a package before I leave home. Typically I do this a week prior to my arrival date to make sure it gets there (and I use UPS so I can track my package). I like to do this because I can pack plenty of diapers, wipes, food, and all items that babies need without having to carry it on travel day. It also takes away a level of stress on the last minute packing because I know the baby essentials were already taken care of. What I like best about this is that I have the products/brands that my family is accustomed to.
Another option would be to use a grocery delivery service. One of the most popular ones for Disney vacationers is
www.gardengrocer.com they offer a much larger selection of items compared to what you will find on property. They have a fairly substantial selection of baby items to choose from.
In the event of a last minute emergency while at the parks, all of the four theme parks have a "Baby Care Center" which offers a wonderful quiet place for feeding, changing, warming foods and they even have a selection of products for purchase such as formula, diapers, pacifers etc.
I hope this is helpful, enjoy your vacation and take a lot of pictures!