We suggest crating the puppy or layering old towels three or four deep on the car seat or on your lap. It is not necessary for you to buy a small crate simply for transporting the puppy, however, as it’ll outgrow it quickly.
The car is a new environment and your puppy will most likely just sleep. If the puppy wakes up and wants to move around, it probably needs to potty. Use the collar/leash combo for stops during your drive. Some puppies will get car sick, so take a trash bag, paper towels, and wet wipes as a precaution. You can additionally layer the bottom of the crate with shredded paper (which I’ll happily provide upon request) to keep the puppy clean if it does get sick.