I travel with my dragon pretty regularly and have done week long trips with him no problem. Not all of them like to travel so I'd do a test drive around town first to see how she reacts. If she seems OK with it, then a road trip with her will be fun =).
I recommend this carrier
https://www.amazon.com/gp/product/B00EW2WKZU/ because it's well ventilated, a good size even for an adult dragon, and it has clips that allow it to be buckled into a seatbelt. It provides a nice secure spot for her when she isn't roaming around. It's safest for her to be in there during the drive but I agree with your vet that regular pit stops to allow some sunshine and exercise are a good idea. This also works well as a spot for her to sleep in a hotel. I used scotch guard on the soft bedding to protect it from accidents. I would also put a layer of fleece or a soft towel down over it to make it comfortable and easier to clean. It's important to keep a bag of cleaning supplies on hand as well. Spray bottle with vinegar, spray bottle with F10SC sanitizer, and a roll of paper towels should do the trick.
I usually carry a tub of black soldier fly larvae with me because they're easy. They travel really well. I also carry ziploc bags with greens and squash so I can put together salads easily. It's best to keep these cold if you can but not a huge deal. You can stop to get replacements easily at a grocery store along the way if needed.
You can bring a basking lamp and either a clamp fixture or an adjustable lamp stand (I prefer this) for the hotel but I found that while it provided a nice quick morning bask, it wasn't necessary. They do pretty well at reasonable room temps especially during the summer. I carried a MegaRay mercury vapor bulb to provide heat and UVB but a PAR38 halogen flood light would work well too and they are a bit sturdier and better for travel. Those just provide heat so time outside for natural UVB is a good idea. Again, if the trip is less than a week it's really not critical to carry a bunch of lighting with you everywhere you go. Especially if you can provide time outside over the course of the day.