Hello fellow granite stater!
Welcome to the Moms Panel and congratulations on your upcoming vacation to Walt Disney World!
We stayed at Old Key West not to long ago and loved the extra space of their very large villas. The resort offers Conch Flats General Store that has a selection of groceries and sundries. You'll be able to pick up basic dairy products, bread, snacks, fruit, cereals and some canned goods.
Another option I would recommend is to use a service such as
gardengrocer to have all of your groceries delivered to you. They have a large selection, and I've heard great things about their customer service.
The last option I would suggest would be to do your shopping for the dry goods/snacks before you leave! I often pack myself a box with the snacks and goodies that I know my family is accustomed to, and ship it to the resort about a week prior to my vacation. Using UPS ground is very cost effective, and you know ahead of time that the items you need will be there. You can make a quick trip to the resort's general store for the perishables, and you're ready to start your vacation!
Hope this helps, have a great trip!