I think it's allowed
You can bring your dog on park grounds they just cant go in any park buildings like cabins and shelters. I stayed in a tent last year and brought both of my dogs
Ive personally have seen dogs on floats and in the water.
When I had went last week I saw all kinds of dogs there a lot of people had their dogs there but they were on a leash but if you're floating on the river as long as the dog is on top of the tube I just saw a lot of dogs with their owners and the dogs were with them on the tubes I don't think it would be a problem to bring your dog or to have your dog with you everybody had their dog there at the river but a lot of them have their dog on a leash so it would not be a problem to bring your dog everybody had dogs
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