There IS no good way to satisfy a 1 year old for that long! LOL! I say that with not-so-happy memories of just trying to make 5 hour trips and my husband was driving while I was the entertainment.
I can't imagine doing this alone. You are a trooper!
DVDs were always helpful; my oldest especially loved TV (and still does now at 4.5). She could watch those forever with no problem.
My youngest didn't care to watch DVDs; she wanted me to take her out of the car seat and hold her. Needless to say, I tried to avoid road trips as much as possible.
I would try adjusting your sleep schedule a day or 2 before and try to sleep during the day and then start on your trip around 3 or 4p.m. This way, the baby will be up only for a couple of hours... you can stop, get dinner and then hopefully they drift off to sleep while you sail the rest of the way in.
Or, as someone else suggested, get up early in the morning and do it that way. I always hated getting kids up and into a car seat that early; mine wouldn't go back to sleep easily.