In short, the sky, and no I'm not talking about the afterlife. When your pet dies it is instantly resurrected and held in limbo until five minutes after it's death, where it is safely transported back to you.
Well in the situation you wanna commit a homicide on your friendly companion, psycho all you have to do is bring your pet with you to a Soul Sand Valley in the nether! Where you can murder to your heart's content! ❤️