I don't remember if they sell the postcards there, but they sell them at the gift shop on the ship and on the shop on CC. The post office is near where the ship docks and the CC gift shop is a tram ride away.
They sell stamps. They don't sell postcards. You'll need to buy your postcards onboard or at "She Sells <strike>Seashells</strike> and Everything Else" (the on-island gift shop).
GET UP TO A $1000 SHIPBOARD CREDIT AND AN EXCLUSIVE GIFT!
If you make your Disney Cruise Line reservation with Dreams Unlimited Travel you’ll receive these incredible shipboard credits to spend on your cruise!