We have used my grandaughters baby carseat when she outgrew it for the past 8 yrs to ride our babys. It works fine. Matter of fact I strap 2 of our 5 lb. babies in it and they love to ride, are very comfortable and safe.They each wear a harness hitched to the strap on the carseat back. So if you can't find any fancy dog seats, a baby carseat will do the same in the back seat of course. I'd never ride them in the front, if the airbag went off it would probably kill them.
Sorry to hear about your accident and glad nobody was hurt, but there is a lesson here for others to think about and thank you for sharing your incident. It might save lives someday.