Just wanted to chime in from experience... Minimum transfer time is important, but 1 hour and 6 minutes between flights is if everything goes well. The 2 times in my life that I had to connect in MIA (on AA), I had issues. And they were both related to not having enough time between flights.

For LGA-MIA-CUR we had an hour between flights. We landed in MIA early, but had to wait for the gate to clear - more than 20 minutes. Not only that, we landed on one side of MIA and the flight was taking off on the other. We ran across the terminals only to see the aircraft push back.

For LGA-MIA-PUJ, we also had about an hour between flights, but was delayed taking off at LGA. We barely made the connection. Our friends that were with us only had one seat available (I think it was given away 10 minutes before the flight) and they stayed behind in MIA overnight. Arrived in PUJ only to find that our luggage didn't run as fast as we did and didn't make the connection. Our friends were kind enough to bring our luggage to the hotel the next day. I wore NYC winterwear in PUJ for about 16 hours.

The reason I mention this is, to be safe, I would double that minimum connection time and put more time between flights especially since you're taking two carriers so that your trip would start out well.

Also, don't forget that Delta also has JFK-MIA flights that you can consider.