We drive straight through to Orlando and always have with our children: the youngest age was when my little one was four months. We find it's best to leave NJ in the early evening, stop for dinner and then settle kids in for night. They sleep right through the night, and because they've been "out" for the majority of the travel, aren't whining about being in car so long. After a fun brunch (at Cracker Barrel, of course), there's not too much to deal with in driving after that and they are so excited about getting to Disney, it has never been a problem.
Of course, driving home is different...I don't think I could take that because there is no vacation to look forward to. So, we take the AutoTrain from Sanford to VA and drive from VA. That is a vacation in itself and is often the best part for the kids.
Last July, we drove straight to HH at night and that was just fine. The drive home seemed endless, though, without anything to look forward to. We said if we did that again, we may stop in Wash DC area for a night for a break.
Basically, our theory is that it is better to have kids sleeping (and quiet) during a long drive than have them wide awake the majority of the trip. It makes it easier on all of us in the long run. Our road trips have become a family tradition and a source of great fun and memories.
Have a great trip whatever you decide to do!!!