I seem to remember buying stamps and posting cards in the hotel on I-Drive (QIP), There was a small shop in the hotel that sold stamps and a post box in the lobby - could be my memory playing tricks with me though (I'm getting old!).
I certainly bought stamps from the shop in POR though and then took the cards to post in MK.
Here's more info:
You can send postcards, letters and packages from all Disney Theme Parks at the following locations:
Disney Theme Parks also have mailboxes where you can drop stamped postcards and letters for delivery via U.S. Postal Service.
Postage stamps are sold at all Walt Disney World Resort hotel gift shops. They are also available: