There is no such Biblical evidence. To the contrary, it is made clear that God treasures His creation from the beginning — ALL of it (not just the two-legged ones!) The covenant made after the flood included the animals; and it is clear that ALL of creation groans for redemption -— (not for “nothingness”). Yes, the Bible was written for man because animals do not need salvation. Their souls are not in jeopardy. Scripture makes it clear that animals will be there — in Heaven and the new Earth. This was accepted by most noted theologians and preachers for centuries. It’s only been the last 100 years or so where mankind has gotten so big for his britches that he’s concluded he’s the only thing that matters. No doubt about it. Animals, like humanity, were created to be eternal. They precede man in the Garden...and death was not part of God’s plan. What He has intended will come to pass.
Actually, does it apply if “dogs” are really man-created? Wolves, foxes, hyaenas, coyotes, all God’s creatures. Are dogs really from Eden?