Maggie May got carsick from day 1. She threw up the 45 minute car ride home when w picked her up.
Once she figured out that she could stand up and look out of her snoozer car seat, she didn't get sick anymore.
You should considered getting some type of carseat as it is much safer to have your baby straped in than riding in your arms or lap. Anything can happen. For the cost of a harness, it is just not worth it.
The snoozer came with a strap that snaps around the seat belt and onto their harness. I would like to get them a riding harness however because in case we should get into an accident, it is better designed/fitted around their chests to prevent harm.