If you book the Nassau Dolphin Encounter directly with Blue Lagoon, children under 4 are free and can accompany you during the encounter. As long as your child won't be totally intimidated by the size of the very gentle dolphin, that's really the safest bet.
The observation area is about 10 feet above, and directly behind the encounter platform. I would be very hesitant to leave a child up there without adult supervision, as it's not really a direct line of sight while you're participating in your encounter.
For the encounter, everyone with that time was together for a brief orientation and educational segment. The group was then divided into smaller groups of about 30 people per trainer. Once we got to the encounter area, we were told to sit along the edge while the trainer reviewed a few directions. During that time the dolphins were swimming in from the lagoon to visit with us on their own. My DD was kicking in the water, and the dolphin looked at me for approval before splashing back. (NEAT!)
The trainer then had each family or group enter the water for a family photo with the dolphin. We were able to pick who got the kiss from the dolphin for that photo. That process went quickly. Then the trainer divided us into groups of 7-10 (maybe 2-3 families per group), and the first group (us!) entered the water to stand on the encounter platform. Those waiting sit on the edge of the encounter area to watch. The encounter area is essentially a large square dock with a square cut-out swimming area in the middle. The swimming area is part of the lagoon, not a contained pool. There's a platform in the water which is about thigh deep on an adult, but can get deeper as the water moves and sloshes. The water was chin-deep on my daughter, but she was fine holding our hands or standing on our feet for extra height.
The encounter consists of touching the dolphin's body, each person touching the dolphin's teeth, getting a kiss on the lips, a hug, and the chance to dance with the dolphin. The trainer we had conducted the encounter in an almost comedy-show fashion, throwing in behaviors (like having the dolphin make rasperry noises at little boys) and silly family-friendly comments. It was funny but educational and amazing all at the same time. Since the trainer was on a microphone system, those waiting their turn were enjoying watching and listening to the "show" that was our encounter.
When we were finished, we were sent back upstairs to the viewing area to watch our encounter on the closed-circuit TV with the option to buy a tape of the encounter. The photographers also printed the family picture and individual pictures which were available for sale.
On the way back to the Wonder, we knew to ask the captain to take us back to the cruise ship dock, which he did after dropping passengers back at the Paradise Island Ferry terminal. (There's a great thread from last fall which details the transportation aspects. We followed those directions with great success, and felt safe the entire time.)
My kids still talk about the dolphin excursion with great enthusiasm, so I'd definitely recommend it even for kids under 4, particularly those who love animals.
