-They're cute. This is the most obvious qualification. If your dog isn't aesthetically pleasing, I don't want it popping up on my feed. And no, your little rat dog isn't cute. I have the same viewpoint on dogs as Ron Swanson:
-Be creative with your captions. Generally, Instagram is for humans. I don't mind when people make bad jokes in their Instagram captions (I am standing in the most fragile glass house in the world as far as bad jokes are concerned), but I'd rather see people go straight up no caption than have them just put something boring like "Vacation with the fam! Love the beach xoxo." There is a pun to be made on every situation ever (Not saying that the puns will go over well, but they're certainly there). Anyway, I want to believe that your dog has a distinct personality-make jokes about how much they love to bark at the UPS guy, or how they like to lick their own butts. I want to feel like the dog is behind the screen trying to make me laugh, debating whether or not the make the played-out but classic pun about life being "ruff."
Only if you and your dog meet these qualifications should you even consider making your dog an Instagram account.
Coincidentally, my cute, poorly-behaved dog somehow figured out how to work a smartphone and made herself an Instagram account last week. She's firing off some adorable pictures with fire flames captions. Follow her @lolagjoyce