You can't swim with dolphins at Disney. That is SeaWorld. They have some type of dolphin encounter but you do not get in the water with them. If you look on the DIS homepage you should find the info. you are looking for.
oops I"m wrong you DO get in the water, just not swim. The info. is under theme parks, backstage tours:
Dolphins in Depth: Here's your chance to get up close and personal with a playful Dolphin. Youll first explore the backstage areas where these amazing mammals are cared for and learn about the research being conducted at Epcots Living Seas pavilion. After this portion of the tour, youll enter into waist deep water to interact with these fascinating creatures. Youll receive a photograph with the dolphin, refreshments and a T-shirt. PLEASE NOTE: No swimming or SCUBA diving is required. No cameras or jewelry are permitted and expectant mothers cannot participate. The dolphin determines the level of interaction.
It says you have to be 13 years or older. Bummer.