As PP mentioned, you do not need to be able to swim to "swim" with the dolphins. My daughter was 7 when we went and the youngest in our group and she was able to stand fine in the water.
Also, when you get to the part where the dolphin pulls you, you can do it in either the deeper water or shallow water. There were 9 in our group; our family plus a family from Ireland with 2 girls around 9 years old. The 5 kids and the 2 moms did the deep water swim and DD and I did end up treading water for a while as our dolphin decided to spend some time checking up on the other groups first before doing our swim. But, the 2 dads were both nervous and did the shallow water swims. So, at no point were they where they couldn't stand up. It's the same experience - one just has you going from deep water to shallow where the other has you going across the pool staying only in shallow water.
As far as everything else, there are life jackets in all sizes that can be used in the other swimming areas as well.
It was a blast!