we've driven down for the 16 hr. drive 3 times with our kids (at 2, 2 1/2, and 3), and we're doing it again next month at 3 1/2....i LOVE the idea of driving at night/early morning, but before you plan on that, please make a practice run!!!! our kids, sadly, do not sleep well in the car and it would be SO miserable to have whiny, tired kids on the start of a magical vacation (thankfully, we learned this lesson NOT on our trip down, but much earlier on other, shorter trips!)
that said, we all try to get a decent night sleep and get the kids up and hour or so earlier than usual (in the hopes that naps will be unavoidable!). we try to be ready to leave within 10 mins. of getting the kids up, but we do take time to find the gift that tinkerbell leaves for us (i don't know how she knows each time that we're leaving to go to WDW, but she always does!)...we have to follow the trail of pixiedust to the gift(s). the morning of our last trip, she left each of the kids a little bag with a small game inside for the car ride. i have it on good authority

that the morning of this NEXT trip, she'll be leaving the Peter Pan DVD for the kids to watch in the car on the way down!
i usually pack way more garbage than i need for the trip (tons of little toys, a bajillion snacks, small wrapped presents, etc), and i generally find that i need about 1/8 of what i bring! a dvd player, i'd say, is essential. we also stop every 2 hrs. or so to let the kids get out and stretch (can't say enough good things about stopping at a hotel to use a clean bathroom and have the little ones walk up and down some stairs...my kids love this and it tires them out---we always ask hotel staff when we walk in if it's ok, and we make a HUGE deal out of reminding the kids to be quiet).
we do not drive straight through, though, and stop about half way down. it adds SO much more time to the trip, butmy kids NEED to get plenty of good sleep prior to a WDW trip where they just go, go, go(oh, how i WISH they were like me and could sleep anywhere at anytime!)
have a great trip!