I have done the trip from the Northeast to Florida around 30 times, the worst trip on a boat with 300 mile range, leaving Florida on a Monday at 9AM and arriving in New York harbor at noon on Thursday. All my trips have been as a paid captain, only once did a slow pace, enjoy the cruising trip. On that trip we left Florida in mid April, got to Maine in August.
So I would suggest a trip lasting between three days and four months!! Actually a month to six weeks would be a good time to get to Florida, then head to the Bahamas where you can spend a long, long time without ever making the longer cruise further south. Georgetown in the Exumas, Bahamas is referred to as "Chicken Harbor." At around 500 miles from Miami it is still far away and many cruisers with intentions of getting further south never get beyond Georgetown.