Who is liable for damages to a car in an automobile accident where a dog is hit and killed, and how do I go about getting money from the dog owner?

I hit and killed a dog that ran into the road, and caused significant damage to my car. I don't have comprehensive insurance due to the low value of my car, but this car is my only way to get to work, so I need to repair it. The police identified the dog's owner who came and picked it up. My car insurance will not file a claim against the dog owner because I don't have comprehensive coverage, so I'm wondering who I should contact (the owner, his home insurance, a lawyer) to get money to repair my car. I'm awaiting the police report and the assessment of damages to my car from a body shop. Also, the town bylaws state that unleashed dogs are not allowed outside of the owner's private property. I would like to not go through small claims court, but since my car insurance won't handle anything, I'm unsure of what other steps I could take to get damages for my car.