Check out the Dolphins in Depth tour at Epcot! Here is what the Disney Passporter says about it:
"This unique three-hour program highlights the dolphin research at The Seas with Nemo & Friends in Epcot. Guests play an active part in the research as they learn about dolphin behavior. Guests must be 13 or older, and 13- to 17-year olds must be with a participating adult. Offered on Mondays-Fridays beginning at 9:30 am. Cost is $150/person and includes a photo, soda, and souvenir T-shirt. Dolphin interaction is not guaranteed. Park admission to Epcot is not required to participate in this program."
(What they mean by "dolphin interaction is not guaranteed" is that it is up to the dolphin if it wants to participate; they can not force the dolphin.) Also, this says guests must be at least 13, but I have heard of younger kids participating.
I have never done this tour myself, but I have read posts on the DIS with people raving about it. I think the actual part you get in the water with the dolphin is around 1/2 hour, but I could be wrong. And, you don't actually "swim" with the dolphin. You are in water about waist(?) deep and you just stand there and do little tricks with the dolphin. It is still an awesome experience, though (I have done the one at Discovery Cove).
Hope that helps, and I'm sure someone else here can offer more on this experience!