The problem is there is no other insurance to collect it on. Legally, neither the homeowner's insurance nor their auto insurance policy is involved, since it didn't happen on their property and it didn't involve their car.
I was wrong when I said your insurance would take care of recouping from the pet owner. Given the circumstances, they are liable, but their insurance isn't.
If you want your car fixed, get it fixed under your auto insurance, or pay for it out of your own pocket. Either way, once you've done that, you can sue the pet owner to recover your damages. Their pet caused it, you have a police report to that effect, so it shouldn't be too tough a case. It's just a matter of whether you want to go through the trouble.