I only have my own experience with Spockie several years ago, but it went well, just he and I, moving from Massachusetts to South Florida. I had him in his cage that fit across the back seat of my car at the time, with it outfitted with his litter pan, tons of hay, a deep bowl for pellets and a water bottle that I think I tried to situate over a crock to catch drips. That was impossible, and his little feet got damp, so be sure to scatter that litter around the bottom so it will soak up the drips and spills. I packed a duffle bag of supplies including trash bags, then brought him in his carrier into the hotel rooms. I let him roam around the bathrooms, but he really didn’t get much exercise for the trip. It’s not so hard on them to be in a confined area for a few days as long as you can let them out at night for a while indoors. The pen is best, but not outside. If you can set it up in the room you’re in, that’s nice for sleeping and exercise. With 2, it’s harder to control them both, so even harnesses are a bit tricky.
I wouldn’t worry about them refusing to eat. Keep the hay and pellets and water always available in their space in the car, then give them some fresh greens, or something firmer like washed carrots or the less wilty greens like kale bunches if you want to keep it handy in a baggie in a cooler. They can have the litter pan changed out at night or even rest stops if you just bring fresh along with you. The mid-sized or even the smaller versions of Carefresh travel well, absorbing moisture and odor in the car. A smallish cooler, like for the beach, with bottled water and ice packs can keep all of you in good shape. I would take Spockie in his carrier into rest stops with me, for fresh air, A/C and safety, but there were other people and pets around so I didn’t want him out among them. They will be afraid if too exposed. The hotel rooms were more secure feeling.
You really don’t want them outside at all in Florida. It is already in the 90s here midday, plus there are some seriously experienced hawks in the air at all times, and the risk of capture by a predator is very, very high in FL. I saw a crow take a baby duckling last year right near my apartment. The mother had wandered away briefly. It’s pretty humid, and unlike their wild rabbit counterparts, they cannot burrow into cool ground and protected cover when out in a covered hutch or cage. It’s just brutal for them, so it’s a good place to be a House Rabbit.
Welcome to FL! I have not regretted the move, and hope to never have to shovel again.