There's no fountain service of it, but you can buy Dr. Pepper at the Swan and Dolphin quick stores - Fuel and Java - in bottles.
Also, the last time I checked, Rainforest Cafe in Disney Springs still offers Dr. Pepper on their beverage menu - in fountain form. NOT the one at AK though.
BTW - I notice when I'm at the DVC lounges with the freestyle machines that Mr. Pibb seems to be a very popular choice. I wondered why, as I honestly have never seen Mr. Pibb on sale by me at any store, and know no one who drinks it - yet every time I'm in the DVC lounges, I see it up on the screen with multiple people choosing it. I asked about it and was told it's Coke's closest flavor profile to Dr. Pepper - most who were choosing it wanted Dr. Pepper and it was close enough for them to choose it over Coke.