Hi Sun,
This is an unfortunate situation and one that is really just down to bad luck. And unfortunately, the car insurance claim is also quite common.
If you were negligent in not securing your dog (e.g. not closing the doors when taking the bin out and not training your dog to stay within your yard) then any damage caused by your dog is subsequently born by you as the owner. The issue is whether you were negligent in what you did (or omitted to do).
In short, pet owners can be responsible for damage caused by their pets, including any car accidents caused by that pet if such accident was unavoidable.
