You've actually got several choices.
1.Ship a box down before you leave right to the resort.
Box of cereal
pop tarts
cookies
hard candy like lifesavers
juice boxes
peanut butter
jelly
rice krispie treats
Head over to either of the HESS stations on property to buy water-usually on sale for a decent price. They also sell milk and soda, bread, snack items, etc.
2. Rent a car for just 1 day and hit PUBLIX, SuperTarget or Wal-Mart. There are rental companies like Enterprise right on property. You could make this an off property day. Leave early, sight see a bit around Orlando (we actually have quite a bit for you to see!) grab lunch at Chilis or Orlando Ale House (great food and a great kids menu) Shop at the Outlets for souveneirs or great deals, grab dinner at Bahama Breeze or even Golden Corral, stop for the groceries on your way back to the resort. SuperTarget is open til 10pm, PUBLIX 10 pm, Super WalMarts are 24 hours.
3. Spend a small fortune and eat all your meals at the resort or at the parks.
4. Take a service that will allow you a grocery stop on the way from the airport to WDW.