Yeah, pets and children are two completely different things. First of all you're not required by law to keep your children bound up in your yard. Also when a child is crossing the street, even if not at a crosswalk, he's technically a pedestrian and it's always illegal to not yield to pedestrians. A dog is something very different, as said a dog is technically property and doesn't have any "right" to cross the street anywhere it wants. They're legally supposed to stay in the owner's yard or with owner on a leash. (Dog parks not withstanding.)
The owner failed to keep their dog under the confines of the law and are responsible for the injuries sustained to the animal and the damages to the car. I agree with what other posters said, the insurance company should handle this it's what you pay them to do. File the claim and you should be all set barring extreme circumstances and even then I think the insurance company will take the action necessary to get payment out of those liable for the accident.
Look, no one feels good about the death of the animal but at the end of the day there was still damage done to you and it happened because the pet owners were not responsible and acting inside the law by keeping the dog restrained. You shouldn't have to pay for it either out of your pocket or with higher insurance premiums by filing a claim against yourself.