I have done this very drive many times with infants, toddlers, preschoolers...now even with all three.
Definitely plan on sitting back with him a fair amount of time. It's tiring and boring for you, but works. I sing, make silly faces, play lots of finger/tickle games. Try checking out Gymboree's "Baby Play" from the library or buying it. It has lots of good ideas.
I get concerned about night driving too, so we leave really early, like 4 or 5 am. We're awake but baby usually sleeps for awhile. If you can't do this, plan around nap time. There's not a lot of good stops between here and Des Moines so sleeping on the front end is really helpful.
Have the car gassed up and pretty much packed the night before. Have snacks for all of you ready to go. Our rule is we try to never stop unless the baby is crying, so no stops for breakfast just because we want it. Also, we consider stopping the kids' chance to run around, so we don't just go into a restaurant and sit down. That probably sounds obvious but it took us awhile to figure out.
DVD players are awesome and well worth it, but a 1 yr old isn't going to watch for hours. Still it will buy you a 1/2 hour now and then and that is beautiful.
Okay, now my suggested stops with kids:
I'm assuming you are going 35 S to Des Moines, then 80 W to Omaha. Cabela's, near Owatanna, is great for little ones to walk around, but it's not too far into the trip, so we usually don't stop there. Sometimes on the way back it makes a nice final stop, though.
Once you make it to Des Moines, there is a welcome center on the west side, right by where you get on 80W. It's marked as a welcome center and Living History Farm. A great stop since it has a Machine Shed restaurant, very family friendly, and the kiddo can run around in the welcome center to work off some energy. It takes us about 4 hrs exactly to get to this spot from Mpls.
Stuart, IA is about 20 mi or so past the welcome center. It has a Burger King and McDonalds both with indoor playareas, plus an outdoor playground.
At that point, you are less than 1.5 hrs from Omaha, so we rarely stop after that.
Also, the Omaha zoo is AWESOME, in case you hadn't planned on stopping there.
Feel free to send me a pm if you want more ideas. Oh, and if you are going via Sioux City instead of Des Moines, I know a mall with an indoor playspace. I could find the name if you want it.