Hello Valerie and thanks for asking the Disney Parks Moms Panel such a great question!
How fun for your dear daughter to be arriving at Walt Disney World Resort a few days before you! I'm sure she'll perhaps have time to check out lots of magical must-do experiences you can enjoy together such as the unbelievable
Pandora - The World of Avatar at Disney's Animal Kingdom Theme Park.
As the current UK Mum here on the Moms Panel I'm happy to share that in my own experience most businesses in the USA including those at Walt Disney World Resort do still indeed accept travellers cheques in place of cash or as a form of payment when accompanied by a valid form of ID. In addition for Guest convenience travellers cheques may be cashed at each Disney Resort hotel
Lobby Concierge.
It may also be helpful to know that
Disney Gift Cards can be purchased and used in place of cash at most locations including for dining and merchandise right across Disney property and the most magical thing is, they don't ever go out of date!
Wishing you and your daughter a magical upcoming trip to Walt Disney World Resort.
~ Jane