Is $45,000 too much to pay when your dog kills the neighbor's cat?

I say absolutely not. Obviously, anyone can get a new cat free, so the replacement cost is nothing (unless it's a fancy breed). The linked article emphasizes the emotional harm to the owner, who was, as people are, quite attached to her specific pet.

But what I would emphasize is that people with dogs should not be letting them run loose. Unleashed dogs terrify children and disturb many adults. Back when I used to walk to work, I permanently altered my path the second time I saw two dobermans run out of a particular house. And there are many cases of dogs mauling children to death.

In short, damages have a deterrent effect, and letting dogs run unleashed in a residential area is a very specific behavior, quite susceptible to deterrence. I hope a lot of people get the message.

Now, about that cat. It shouldn't be running around loose either. It might easily bite or scratch a child too. And, worse than a dog, it is a nonnative animal that hunts down the native animals to the detriment of the ecosystem. Maybe someday someone will sue the neighbor whose cat kills a nesting songbird in his yard and win $45,000. What would you think of that? I say it would have a fine deterrent effect.