Direct Duties & Indirect Obligations

I think that most people would agree in societies day and time, we all have certain duties that we are expected to uphold, a direct duty. For instance, if we see a man hit a woman, although some would ignore the situation, one's direct duty is to defend the woman from the man and report the man to higher authorities. That is because it is each person's independent duty to defend another sentient being. But why then, should I report someone who kicks my dog, who is not a sentient being. I love my dog, but he doesn't have the same complex emotions or thought processes as a human, yet I am bound by an indirect obligation to my dog to defend him. That is because, although my dog is not a sentient being, it would reflect on me, and show others that if I don't defend a non-sentient being, that I have the capacity to allow the same injustice to happen to a sentient being. Well, that's the argument according to Kant. Is he right though? Do I need to fulfill indirect obligations to prove whether or not I have the capacity to fulfill my direct duties, should I need too?