i strongly disagree!
the fact that you do not know the animal that was killed in order to make a medicine, does not make it ok to kill her, or even lower it's priority below your pet.
if i had a child who needed a heart transplant, as desperate as i get, i will never consider killing a child i don't know in order to take his heart as acceptable.
life is tough, inevitably we and our loved ones lose things, but living without ethics and compassion is the greatest loss of all.
bare in mind that even if you try every immoral option you have, he may still stay sick, and undoubtedly die, as all living things do,
then you have lost twice.
if the problem is only the pain, then painkillers are the most ethical, and well tested solution.