You do not have to travel with your pet in a way that makes you worry about their safety. In fact, if that is what you are going through, then you are probably doing something wrong. Your pet's safety should be a top priority.
Make sure you strap the pet into the backseat in such a way that they won't go sliding around the vehicle or otherwise get hurt. You should never put them in the front seat with you even though it might be tempting to do so. The front seat is a lot more dangerous for them, and you could get them seriously injured or even killed if you try to do that one.
Additionally, it is up to you to make sure your pet has enough food and water brought along with it for the entire journey. They will require a lot of stops potentially, and it is best to keep them well-fed and watered.
