Pets distracting the driver are an extreme hazard. Riding unsecured is very dangerous also to your pet. Fresh water and food are also a necessity. Bring water from home to prevent possible gastrointestinal problems when traveling. Breaks are needed along the way.
Most rest areas provide pet areas.
Always keep your pet on a leash to assure pet safety. For the safety of all others please be sure you bring pet disposal bags for rest stop as well. Make sure to remember heat in cars. Even with windows rolled down heat is trapped in a vehicle much like a greenhouse. It takes only minutes for the interior of a car to become much hotter then the outdoor temperature.