Agreed, make sure that their travel carriers are well-secured in the car so they don't go flying around the car or falling on the floor of the car, and make sure that there is nothing loose in the cage like hanging-toys that they could get stuck on or hit with.
Make sure that you have blankets/towels to cover their carriers with, and keep a watch on them while on the trip to make sure they aren't getting very stressed or upset by the noises and such, if they are you should cover them.
Bring plenty of bottle water and food for them, 18 hours is a long trip and they'll need plenty to drink and eat, and don't be surprised if they actually refuse food during the trip, sometimes they do and sometimes they don't, but you must be prepared to feed them and give them plenty of water to drink.
I'd also try to make a few short stops along the way, just so you can spend a bit of time talking to them, maybe bring their travel carriers out of the car for a little fresh air (DO NOT LET THEM OUT OF THEIR CARRIERS OBVIOUSLY!!!)
Some birds do get motion-sick or car-sick, so if either of them vomit in their carriers that is most-likely why. Also be sure to put something in the bottom of their travel carriers, such as a towel or blanket, and be sure to bring extra, clean towels and/or blankets to replace the ones inside the carriers as they get soiled, so that your birds are not laying in/sitting in/walking in poop.
I don't know if you're driving straight through to NC or if you're staying overnight in a hotel that allows pets, but if you're staying overnight in a hotel it would be a good idea to secure the room completely, be sure the door is latched and locked, cover all mirrors and pull the curtains to the windows, and allow your birds to come out in the hotel room to spread their wings and get some exercise. If you are driving straight-through, as soon as you arrive to your new home, be sure to do the same, secure a room completely and let them out immediately so they can spread their wings and get settled in.
They'll be fine as long as you're prepared. I drove my Senegal Parrot, Kane, back from Raleigh, NC up to State College, PA, when he was only 10 weeks old and still on 1 hand-feeding a day (nighttime comfort feeding), I picked him up from his breeder around 9:00 at night, and then we spent the night in a motel room, bonding and snacking, lol, and he slept on my chest all night, and we left early the next morning and went on the 8+ hour drive home to Pennsylvania. He rode the entire way home on the back of my neck, in the hood of my hoodie, lol, while I listened to an audio book. We stopped at several rest areas and he went outside on his Aviator Harness (luckily his breeder had trained him from very young), and he basically slept the entire way home except for the rest stops when I got him outside on his harness. So your birds will more than likely sleep most of the time anyway, and be in their new home before they even realize they were on an 18 hour drive...
