We use a dog harness that attaches to the seatbelt (found it at Petco) for our Sheltie and use a small kennel mat on the seat bottom. He sits quietly as he cannot move much and cannot scratch the seat.
Your dog must be a saint! I have the harness as well but he won't sit still and is constantly trying to climb into my lap. I admit I could have trained him better but he is a Pug and they are not very easy to train! Seriously, I need a car condom. I need it to cover the passenger door, the entire seat, the center console and my lap! No, I'm not kidding!
I have a yellow Lab and have taken him in the car only a few times. I use a sheet to cover the back seat and floor. It catches his hairs and protects the leather from his big claws. He's very good riding though. He sits the whole time with part of his head sticking out the window.
the DG DLX pet travel hammock is really nice. It doesn't cover the doors though . . . but so far so good on that one. I have a German Shepherd and Boxer and they both travel with me sometimes. The GS is fine but the Boxer tends to like to slobber and chew on everything, so he has to be watched closely.
My pit bull takes up the back seat. Went to Calico Corners (fabric shop) and bought black denim. I sewed a seat cover that loops around the 2 head rests and even covers the back seat floor. Not only are my leather seats protected from his nails, but the dropped fur mostly lands on the denim. I have an additional identical cover for the center console as sometimes he will stand to see out the windshield. I am lucky he doesn't try to come forward to the passenger seat if it is empty.
I bought a mover's blanket at Harbor Freight.I attached a long heavy weight bungee cord with tarp clamps. The bungee cord loops over both rear headrests and covers the entire back seat. I have two shepards and so far so good.
I have a friend who is a Pug Fanatic and she told me to go to this link for some good ideas. Although I probably would just use a towel on the seats but it doesn't prevent your pug from scratches the seats and doors.
But Check out "In the Company of Dogs" or "Drs Foster Smith"