Traveling about 20 hours with 3 week old?

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First Time Mom- Baby is due June 24. We have a family reunion in Wyoming, in July, which is about a 20 hour drive from us and unfortunately we are driving. We are leaving July 15th to get there by July 18th. We are driving about 7 hours a day, give or take. Making nightly stops at hotels until we are there. Baby will be about 3 weeks old. Haven't talked to the doctor yet, but will at my next appointment.
Anyway, has anyone ever made travels like this? We kind of have to go, but I'm a little worry with baby only being about 3 weeks old (give or take since you never know if baby will be early or late). We will also make rest stops every 1-3 hours (when baby is awake to eat and change and give a break from the car seat.). I am also going to breastfeed if that makes a difference in health and immune system strength. My baby getting sick is what freaks me out the most since she will only be about 3 weeks old. 
Thanks for the insights!