I don't know who drew this but I think it's a Dictator Pickles (Emily Youcis / Alfred Playhouse) rendition of the dog. I like it a lot, and while it's more human than other options, it's still very furry.
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The fun thing about it is you could swap out the hat with any accessory and do specific things with it. I like the idea of the drool being like a waterfall that flings around with the momentum of the avatar.
There's the Animal Crossing thing which is very cute and appropriate but maybe too cartoonish.
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The most esoteric option is going with the album art of Shakey Graves I've ripped and used everywhere for no reason other than
I like this song and it's a cow head.
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Honestly if I had to pick right this second I'd go with the Shakey Graves. You can still add expressions on the cow head as if it's actually part of the character instead of a mask. Since the body is human it's not really furry.