That’s really interesting that the comparison is to dogs rather than moose or deer, I guess both being domesticated was more relevant than the physical appearance? Any chance you know more of the history of the word, or where to find it? I checked the Ojibwe People's Dictionary but it didn’t have much to add to what you already said, etymology-wise.
I did find the word bebezhigooganzhii as a synonym, is that one also a common word or are either of these less used than the other?
Also for anyone who hasn’t heard the language, the link above is to the page for this word and it has spoken examples - it’s a really pretty language.