Yes, cameras are allowed. But you can't take cameras in the water with you during dolphin swim. They said the dolphins try to take them and the cameras are dangerous for them because they could be swallowed.
Fugi film makes these disposable ones. I have seen them at discount chains like Target and Walmart. They are just like the regular cameras except they are encased in plastic- and have a rubber band to keep it on your wrist. Buy them ahead of time because they sell them at DC for about twice the price you can get them elsewhere.