Hello, Stacie,
I have to confess to you that I've been thinking about your question for a while trying to think back to previous trips and if I've ever seen any iron-on patches while at Walt Disney World. Sadly, I don't recall seeing any. However, that doesn't mean that there aren't any.
The
World of Disney at Downtown Disney is the most-likely the most promising option for you with the large size of the store and merchandise. Also, Disney Design-A-Tee and
Disney's Wonderful World of Memories could be possibilities as they offer personalization of merchandise, so perhaps they have some version of personalized patches. You could also try calling Disney Merchandise Guest Services at 877-560-6477 or by emailing at Merchandise.Guest.Services@DisneyParks.com to see if they could help track down the availability of the the iron-on patches.
Out of curiosity, I also did a quick search on Amazon for Disney iron-on patches and did find a variety of them. It won't be quite as magical as buying while at Walt Disney World, but it may be a good compromise.
Sending you loads of pixie-dusted shopping thoughts!
-Kara