Mary,
Immediately adjacent to Walt Disney World property, over by the Downtown Disney area, is the Crossroads Shopping center. At this strip of stores and restaurants there is a Goodings Grocery store that should fit the bill for you. They, like other services in the area, also deliver groceries.
If you have a car, then drive over. If you don't, then web ordering may be cheaper than grabbing a cab, when compared to the delivery fee.
As for ordering from Goodings, I have not used it myself, but if you visit their website at
www.goodings.com you will see how to work it. There is a minimum order requirement, as well as a fairly significant delivery charge. It appears that if you are ordering a lot, it might be worth it.
Another choice is
www.gardengrocer.com. Again, I have not used this myself, but it appears there that you have a lower delivery charge, and can get that waved with very large orders.
Have a magical vacation!