Although your reasoning makes sense, I think it's a good idea trying to memorize the differences. The reason is that "cachorro (male)/cachorra (female)" are widely used in Brazil in songs, slangs and general expressions (maybe more than "cão").
So, even though I understand your concern to keep the learning simple, I suggest you to enjoy the ride and try to learn also the culture difference between Brasil and Portugal :)
Meu cachorro come frango, is roughly translated to "my dog eats chicken" yes?
I input this but for some reason, duolingo is telling me that is incorrect. And that the correct answer should have been "my dog is eating chicken."
Is this relevant? Isn't this just a technicality or preference of how to say the same thing? So shouldn't my response be acceptable?