From dog + -dom.

dogdom (uncountable)

1. The state or essence of being a dog.
   • 2021, Pat Shipman, Our Oldest Companions: The Story of the First Dogs, page 29:

     What the first dogs had, like the last wolves, was what I call dogginess. Dogginess is the essence of dogdom writ large. Clearly the first dogs had dogginess, or we would not recognize them as related to modern dogs, but they certainly were not dogs as we know them now.

• doghood