The safest way to travel with your cat by car is to keep her contained preferably in a kitty travel carrier. Unfortunately most cats aren’t terribly fond of their carriers, but it doesn’t have to be that way.
Place the carrier in a safe place in your house in a spot that is easily accessible to your cat. With the door open, place tasty, extra-special treats in the back of the carrier so your cat has to walk all the way in to get them. Don’t close the door on your cat and don’t force your cat inside. Let her go in on her own, stay as long as she wants and come out on her own. Eventually, she’ll realize that great things happen to her in the carrier.
You’ll find her spending more and more time in there, always reward her with a wonderful treat. Only after she’s comfortable spending time in there with the door open can you slowly start closing the door. Give her a super treat, close the door, and then open it before she has time to panic. Practice giving her treats and keeping the door closed little bits longer each time.
You may only be able to keep the door closed a second longer each practice session but it will all be worth it when you have a cat who will crawl willingly into her kennel for a car ride!