Etymology of "dog-tired"

I have been searching various on-line dictionaries for the derivation of
this phrase. It is amazing that such a commonly understood phrase is
not to be found in any reference I can think of.

What is the background of this phrase? Is there a reason it is not widely
found in dictionaries?

I'll check in my references. The image "dog-tired" conjures up for is that of a hunting dog that is falling-down exhausted and panting after a run in the woods.