Floriday Keys State Parks dog question

We are thinking about going in Feb. 2018. We have not camped down there with a dog. I have been doing a lot of searches on this forum and on the web. Just want your input. I know dogs are not allowed on the beaches. Are there other coast areas that are not considered "the beach" at the State Parks? I recall at Bahia Honda there is a beach on the bay side and another long beach on the ocean side. Surely there is some place around the island that you can go with your dog.

I found that these places are dog friendly. Coco Plum Beach and Sombrero Beach in Marathon, Veterans Memorial park on Little Duck Key, Big Pine Key dog park (really? with Key deer on the island), Dolphin Research center.

Thanks for reading. Any comments appreciated.
Marcia