This article is about Doc's 1955 dog Copernicus. You may be looking for the Moon crater Copernicus.
"While he [Doc] studied himself [in the mirror, wearing the brain-wave analyzer], wondering whether to continue work for the day, Copernicus started barking. The dog, third in a line of pets named after famous scientists, raced from the kitchen into the living room, arriving there just as the rap [at the door] sounded."
Sometime between then and 1985, most likely by 1970, Copernicus passed away and was replaced by Doc's new canine companion Einstein, continuing with the theme of pets named after famous scientists.
Copernicus appeared to be either a mixed-breed or a breed of terrier, possibly a Wheaten.
Behind the scenes
While Copernicus was never referred to by name on-screen in Part I, his name was mentioned in the novelization. It wasn't until Part III that his name was actually spoken and confirmed as being Copernicus.
As with Einstein in Part III, Copernicus was portrayed by a different dog than the one which was used in Part I.
In the novelization (see Quote above), Copernicus is identified as being the third in a line of Doc's theme of pets named after famous scientists — implying that Doc had two other dogs (the names of which remain unknown) before Copernicus.