Book about dogs going extinct

I remember this book that I was read in like elementary school where this boy and his dog find a river where once a stone slab (?) with an animals paw/foot/whatever print reaches the end of it that species goes extinct. The dogs paw print accidentally got sent down so the boy is trying to get it before dogs go extinct. I think there was a villain who saw the boy left a handprint in the mud and tries to cause humans to go extinct as well but that could be wrong