You will be able to begin embarkation at 11:30, but I'd recommend around 2 because the lines will be shorter. Here is a website for a shuttle service in Miami, www.miami-shuttle.com
. They begin disembarkation around 8:00 am, you're normally off by 10:00 am so they can begin boarding the next cruise. It doesn't matter if you use Princess shuttle, they need to have everyone ashore so they can turn the ship around. You will be given colored tags for your luggage and will be called for disembarkation by the colors. Since you're arriving in Miami so late, I think you would be best to get a hotel near the airport as it's a good 45 minute drive up to Lauderdale. Hope this helps. We're leaving on the Sun Princess the same day. Enjoy your cruise!!