M.,
My husband is in the military so I often find myself in the car with my 2 children. You've gotten some good advice. Consider your daughter's personality and your own and pick what you think will work for your family.
My children are within days of being exactly 2 years apart. They are now 3 and 5 and have lived in 3 different places(Virginia, Missouri, and Washington). We have spent a lot of time traveling wether moving, visiting family, or vacationing. Our driving strategties have changed based on their age and wether I am alone or with my husband and wether we have 1 or 2 cars.
One thing to consider when planning your trip is that you will be changing time zones.
Some people have suggested traveling at night - if your daughter sleeps well in the car and you don't mind driving at night, go for it. Just remember you are driving for 3 days and will need some rest, too. If she sleeps while you are driving, what will she do when you are trying to sleep?
I myself am a morning person. My children, too, are their best in the morning. Therefore if I am involved in driving, we usually get up and go right away. Sometimes we even have breakfast in the car. It helps to pass some time. Then we drive for as long as the kids are content. At this time of day they are almost always good for at least 4 hours and someitmes longer. Then we stop for some lunch and find a place for them to play. Then they are usually ready for a nap - in the car they sometimes nap for as long as 3 hours. I usually have a snack ready for them when they wake up to buy me a little more time. Before I know it, we've gone another 4 hours and are ready for a dinner break. If we are traveling for several days in a row, we usually end our day here and let the kids unwind at a hotel after dinner. If we are close to our destination, we keep going after dinner.
For car entertainment here are some things I do. My kids have special animals and blankets that always come in the car with us for trips. I also help them to choose some things for a backpack that they can sit on the seat next to them to play with along the way (these things are usually played with for a while then dropped to the floor or somewhere out of reach - we just pick up and repack at each stop). On the seat next to me, I usually have some small surprise things that I pick up at a local dollar store or elsewhere and distribute them on an as needed basis. I also keep snacks and books on the seat next to me. My children love books and music so we stash the CD player and car with kid appropriate music and bring along CDs that read books to the kids. We do have a portable DVD player that we reserve for long trips so the kids also like to watch a movie sometimes. Use your imagination, too. You can play car games like I Spy, etc.
As I mentioned, my children's ages really have driven our schedule on our many driving trips. The paragraph above describes the schedule we used when we drove from MO to WA when our daughter was 1 and our son was 3. My husband and I drove separate cars. However, my daughter's very first long trip was from VA to MO when she was 2 months old and my son was 2 years, 2 months. On that trip, I was traveling alone. I was lucky, they were great!!!!! Since I was nursing my daughter, I drove until she was hungry. I would stop at a McDonald's where my son could play while I fed her. Obviously on this trip, I stopped more often.
Good Luck on your upcoming trip and move. We too will be moving to MO but not until May. Whatever you plan, remember to be flexible.