Although there as several omens of dogs and death (a howling dog predicts the death of a loved one) there are no omens, I can find, about the death of a dog meaning anything.
The breed of dog in The Omen was a Rottweiler.
It means someone or something indicates impending death/destruction. Think of it as an omen.
It's a death omen
An omen
Belgian shepherd
death i think
historically and religiosly, crows are an omen of death, but vultures are also associated with death
The family dog is a Rottweiler and the dogs in the cemetery were Dobermans
omen
banshee
The hawk was an omen of death in ancient Greece.
an omen or prophecy