We drove 2400 miles and back with our 3-year old, who is a picky eater, and what worked for us was to take a big Coleman cooler (and one of those foldable luggage carts to get the cooler from the car to the hotel room and back every night). I prepared food ahead of time (rice, ground beef) and brought things like frozen broccoli, bread, crackers, and cookies, and kept the cooler packed with lots of ice. We used a thermometer to reassure us that the cooler was cold enough. It worked out even during very hot summer days as long as we added ice a couple times each day. (I used zip-lock bags around the food to keep things from getting soaked.)
Another thing that worked for us was to stop at buffet restaurants (we like Golden Corral), so that we could put a variety of foods on our son's plate, and see what he was in the mood for. That way, we could go back for more of what he was eating, and not waste a huge serving of something that he didn't have an interest in... At other restaurants we just offered him things off of our plates.
He used to eat "baby food" from the jars, and it made traveling so much easier, but he just doesn't like the taste of it anymore.
Another trick we've found helpful is to stay at places with a kitchenette (stove-top and microwave), and bring a few dishes for cooking. We buy things from the local grocery store, and cook a few days worth of food on the road as we go.
Traveling with a toddler turned out to be easier than I had expected! Our son did need time each day to run around, though, and it was usually when we wanted to be sleeping or driving :( One-year olds might need to get out of their car seats pretty often.
I hope this helps!