If you have a newer model car, your front airbags may not deploy with just your pup in that seat. Most newer models have weight sensors in the passenger seat. However, the side airbags could still pose a problem. Cindy (livingdustmops) recently did some research into this. Maybe she'll fill us in!
So far, I am using a special seatbelt harness for Joey that I feel comfortable with. However, he gets carsick so I am planning to buy a carseat for him as soon as I get home so that he can see out!