Hi Libby!
Without regard to where your post should be, ;-) we made the same trip at x-mas time this year. We left WDW at 1 PM, and arrived at our hotel in downtown Miami at 5. Although we didn't take a cruise, we could see the cruise ships docked in the Biscayne Bay (or Miami River-- wherever they technically were docked). We made only one short stop at a gas station on the way.
FWIW, we took Florida's Turnpike, then hopped on I-95 around Palm Beach (I think).
Have fun!