Hi there Susan, and welcome to planDisney!
In my 25+ years of visiting
Walt Disney World Resort, I don't recall ever seeing a FedEx drop box on property. However, I will admit, I never really looked for one!
I ended up heading to the FedEx website to search for a drop box in the area. (Use Lake Buena Vista, FL as the search location.) Although there are a couple of drop boxes on Disney property, they are "backstage" and not in Guest accessible areas.
Your best bet will be the FedEx Office store in a nearby shopping plaza on Apopka Vineland Rd. This location is not too far from
Disney Springs. If you will not have a vehicle, I would suggest using a rideshare service such as Uber or Lyft to reach the closest drop box to where you will be staying.
There is another option if you don't mind a bit of a walk. The Hilton Orlando Buena Vista Palace has a FedEx Office Print & Ship Center. From Disney Springs, use the pedestrian bridge to cross Buena Vista Drive and follow the walkway to reach the hotel. I recommend calling to confirm the location's hours prior to heading there.
I hope that helps! Please let us know if we can answer any additional questions. Enjoy your visit!
Anne Marie