If you leave something like 4-5 hours I think you'll have it covered. I managed to miss the Florida turnpike going from Kissimee to Orlando so it took me a little longer last time . I think the quickest I've done it was about 3.5 hours but you can get a little snarled at times as you approach Miami so I'd leave a little more time to be safe
We did this in Feb. We made really good time until we got to West Palm Beach then the traffic got heavier until it was stop start for the last 2 junctions before the airport exit. We left LBV early and stopped at friends for lunch at Boynton Beach ( I think) Finally did the last section during the afternoon getting to our hotel at about 4pm. I suppose its quieter at other times of the day.
I would say minimum 3 hours, guess it depends on how many stops.
We did it in 3 and a half with one 15 minute stop a few years back, still depends on traffic I guess.