The Keurig Duos use a flat bottom type filter on the carafe side...generally filters are not provided (on occasion, I've had a metal mesh one in there but that might have been a fluke or left from a previous guest) - I always bring paper filters along with my coffee beans and grinder.
The Duo machines can be a little strange on the carafe side as they only have selections to brew 6, 8, 10, or 12 cups in the carafe. When I am there solo and only want to brew 2 or 4 cups, the strategy is to fill the water basin of the machine with only 2-4 cups of water and choose '6' when brewing...it just stops when it runs out of water. There's a little button dance you have to perform to start brewing - hit the Power button, press the 'carafe' icon, press the button for the number of cups wanted, then press the 'brew' button in the center.
Alternately you can bring K-pods if you want to use that side of the machine.
Disney provides several Peet's pre-filled coffee filter bags for the carafe side - generally good for between 4-6 cups each - and a handful of k-cup pods as well. So if you didn't want to bring or buy your own coffee, they do provide some.