We haven't yet driven to FL, but our DS4 is a great road-tripper - first trip he was just a week old (six hour drive) and now we routinely drive to do what we call the "grandparent tour" to visit my parents (NY), DH's parents (NJ - but they just moved closer) and my sister (DC) and her family. Going from the Missouri to DC is about 15-hours, here to NY is about 18.....I've now done the round-trip three times and one one-way (bumped off a flight and just took the rental car and drove back - it was faster than the flights the airline could get us on to get us home!).
Personally, I wouldn't dream of driving straight through - that's way too much butt-time in the seat for anyone, kids or adults! Plus driving does fatigue most people, so safety is my main reason to do no more than 10-hours in a day, split up with good breaks.....so to do MO-NY or MO-DC, we do take one night overnight somewhere in-between.
I try to schedule breaks specifically to give DS something to look forward to - mostly stopping at Children's Museums to play for a while and have a meal....or finding a good park to let him run around for an hour or so. If you wanted to locate museums to stop at, the Association of Children's Museums website is a good resource - and if you're a member of your local CM, you can use the reciprocal pass benefit to get in free to whatever museums you stop at if they're members of ACM!
I try to get out the day we start our trip very early - like 6:00AM or 7:00AM - so we can clock 4-5 hours and then stop for lunch.....usually take at least 1.5-hours downtime out of the minivan and then hit the road again (if we stop around 1:00) 2:30-3:00 and do another 4-hours, stop and have dinner and then do the last two hours before stopping for the night - once we did call it a day after dinner - I was pooped (I do these drives without DH since he has to work and it's me that takes DS to see the family!)
What started our "road-trips" wasn't so much that I like driving - I do, I don't think it's all that bad as long as you're not stuck in traffic! - it was cost....I much prefer to fly and rent a car, and if an airfare + car combo make financial sense, we fly. But a few times now either the airfare was outrageous or the car rental was outrageous.....after sitting down and calculating my cost to drive (including getting oil change before and after type costs), it made sense to drive since we weren't just saving a couple of hundred dollars, but well over a thousand!
I'd almost resigned myself to driving to Disney in September when airfares wouldn't budge, but finally found a good deal and the car rental out of Tampa...out of our regional airport for less than one of the major airports that take us two hours to get to and we have to pay to park at! So, what I save driving to the airport at home, I do when we arrive in Tampa - no biggie.
For our upcoming Christmas trip - I'm already pretty sure, if not with DH going, DS and I will drive.....airfare right now is nuts - like $900/person round-trip out of our regional airport and $500/person out of either major airport....add to that the car rental fees are outrageous - over a grand! - OUCH - so all totaled, it's way less expensive to drive DH's car (a good winter car) than flying and renting a car. Since he can't take off the day we'd need to leave by, I'll probably bite the bullet and fly him down O/W and then we can drive back together --- or just fly him RT (still don't know his schedule he needs to be back by) if needed. Paying that much for one ticket still saves a considerable amount of money overall!