Traveling with a breastfed infant has its challenges, but it is completely possible if you take a few things into account when planning your trip. The first thing to remember is, your drive will take longer than Google Maps claims. Sure, it's 10 hours from San Francisco to Las Vegas if you drive straight through and don't hit traffic, but keep in mind that you'll have to stop every few hours to tend to your baby.
The inconvenient thing about traveling with an exclusively breastfed baby is that you can't feed while driving. With older kids, if they get hungry in the car, you can hand back snacks to them to eat and continue moving. With a baby, you have to stop to nurse. On the other hand, the fact that you'll have to stop to nurse means that you also have to stop to get out and stretch your legs, which is highly recommended on long drives anyway.
The best way to handle breastfeeding on a road trip is to try to feed whenever you stop for another reason, so you can minimize your stops. Or, to look at it another way, every time you stop to feed the baby, also go to the bathroom, grab a bite to eat yourself, or fill up the gas tank.
It's important to put the needs of your baby high on your list. Don't try to push the baby to go longer than she normally would just to get in another half-hour of driving (unless you're looking for a safe place to stop, of course!). This can be harmful for your milk supply as well as causing the baby unnecessary distress. Don't rush her to finish a feed or push her to eat more than she can. Remember that, just as it's necessary for you to get out of the car for a bit, it's not good for her to sit in the car seat for many hours in a row. She needs to change positions, look around, and exercise those muscles. She also needs human contact. Sitting backward in the car seat, she doesn't see you or feel your touch. Keep her in mind as you drive!
On the flip side, some babies like being in the car and will sleep more than usual, causing them to eat less often than they would at home. If this happens, you'll need to protect your milk supply. If you can, bring along a manual pump or even just a bottle you can hand-express into and pump either at stops or even while driving (if you're a passenger, of course!). Remember that a baby who eats less during the day may make up for it by wanting to nurse more at night.
Another option to consider is to drive at night. If the view isn't part of the drive, but rather the drive is just a means to get to your destination, consider doing most of your driving early, early in the morning or late at night, when the baby would normally be sleeping anyway. This way, he can sleep in the car, and you don't have to worry so much if he doesn't eat as much on the drive. If you do this, make sure you're well-rested enough to drive safely, of course.
Do NOT nurse while the car is in motion. It can be tempting to sit next to the baby, unbuckle your seat belt, and lean over the car seat to dangle a boob into the baby's mouth while someone else continues to drive. This is dangerous. If you are in a crash or a sudden stop, your body can act as a projectile directly into the baby's face, crushing him.
Get used to and comfortable with nursing in public if you're taking a drive with your baby. You'll find yourself having to breastfeed at rest stops, vista points, restaurants, and gas stations. I do enjoy nursing in the car (while the car is stopped, of course). I find it's comfortable and relatively private. Allow your baby to take all the time he needs to complete the feeding, and take the time yourself to relax a little and reconnect with your baby.
See my Family Road Trip playlist on my YouTube channel for lots of related videos, and especially see this and this for examples of nursing and pumping on a road trip.