I think flying is the best option. I did it with my baby when he was 3, 4 and 5 months old. What always works for my is feeding my baby when the plane is taking off so he can fall asleep and doesn’t get bothered by the pressure on his ears. Also most airlines allow you to take the stroller for free, you can have it until you’re boarding (last time they allowed me to take 3 pieces, the stroller, the carseat and a seat that attaches to the stroller). And also they don’t count the diaper bag as your personal item so you can still take a separate personal item besides the diaper bag. And definitely have a few toys so your baby doesn’t get bored and starts crying. Good luck! :)
We always fly to Florida! It was super easy last time with my husband coming as well. We pushed my baby around in his car seat/stroller combo until we had to board. Then we could easily gate check his car seat/base and stroller piece. It was sitting there as soon as we got off the plane so we could use it again in the next airport.
My little girl is 5 months and we just made a drive from Minnesota to Texas and it was 19 1/2 hours (longer with the stops and such) we just made sure to stop and get her out of her car seat at LEAST every 2 hours, changed her and fed her