Hi Natalie, welcome to the Disney Parks Mom's Panel!
Walt Disney World does allow guests to
bring snacks and water bottles into the parks and it is a great way to ease your days at the parks.
For getting stuff to your resort I recommend sending some boxes from home and ordering from online stores like Garden Grocer. The delivery charge is basically covered when you order a box of water bottles.
All Disney Resorts feature a convenience store on their lobby, were you can buy milk, bread, cereals, toothpaste, nail clippers, children medicines and many other essentials.
Thank you for visiting and letting us help you plan a magical Disney vacation.
Hope to hear again from you.
Miguel