Terry, you are not going to find cabins in Miami--Miami is a large city. You will find cabins down in the Keys. I can recommend Pelican Key Largo Cottages and Sunset Cove Beach Resort. Both are old Florida, allow pets, and are reasonably priced. Sunset Cove is the nicer of the 2. They are close to each other as you go down the Keys highway.
2015 AI 2, 2014 Tandem
"Any intelligent fool can make things bigger and more complex ... It takes a touch of genius and a lot of courage to move in the opposite direction." A. Einstein