Hi Anna!
Welcome back to planDisney.
It's always a pleasure to assist my fellow guests from the UK, and I'm so excited to see that your holiday is just around the corner!
I love that you are sending postcards back home! This is something I used to do and now with social media and instant communication I have stopped - you've reminded me that this is a lovely thing to do - everyone likes receiving postcards through the letterbox (even if they don't arrive until after we are home....). You'll find postcards for sale all over the resort, with maybe the best selection at the larger gift shops such as the Emporium at Magic Kingdom Park or Creations Shop at EPCOT.
Specifically at your hotel -
Disney's Art of Animation Resort - your gift shop "Ink & Paint Shop" will likely sell postcards and stamps, and you can always purchase stamps at the Front Desk of your hotel. Once stamped, you can give them to the Cast Members at the Front Desk for posting.
For an extra sprinkling of magic, if you visit City Hall on Main Street U.S.A. in
Magic Kingdom Park, you can request a special "Mailed From Main Street" stamp on your postcards before you post them (you will need to add postage stamps as well). There is a mail box right outside City Hall.
Other locations that sell postage stamps around the parks, and Disney Springs, can be seen here.
Please come back and visit us if you have any further questions, and you can
send me a direct question if you wish. We will be happy to help you plan your magical holiday to Walt Disney World!
Sue