What makes you think that you could have prevented it?

Try and think, that even if you had done something differently, what happened could have happened at another time, or another day. As hard as it is, you can't change what happened, but to accept that it wasn't your fault, you also need to accept what has happened. Whenever someone's born, they die too. It isn't easy, but it's a fact of life, but a fact that you don't have control over. If you had control over it, then it might have been your fault. But since you don't, it isn't. You didn't physically kill your dog. Like you say it was an accident, and an accident that wasn't your fault.