OK, thanks! So it's pretty much the same as I saw on Key Biscayne's Hobie Beach, which allows leashed dogs. Pretty much everybody there disregarded the leash requirement early in the morning and late in the evening.
I like to stopover in MIA enroute to LAX when I travel with the dog in the winter ever since AA has inaugurated their MXP-MIA service. Minimal risk of weather-related flight disruptions. I usually stay at the Sofitel there, though. Reasonably priced and dog-friendly (no pet fees!).