"First, there needs to be good reason to own a dog."
Well, a little help in the fights, and a big help to outdoorsman, like actually in fact.
"Second, breeding dogs should be accesible enough to be worth the effort."
2 dogs + stock of meat, pretty accessible if you want to, after it's pretty much matter of time.
"Third, breeding dogs should yield some advantage over just buying them (this contradicts 2, but you've already given something)
Sell and/or use them, they are dogs man, what do you want more from them ?
"Fourth, breeding process needs to be exactly designed. Bringing stuff to tent is not exactly interesting, and it'd better be multiplayer action - like getting kennel in your base Smiley."
Well it was meant to be a "little addon" to the game, little supplement of soul, commerce and companions, not a big exciting part of it, like a new profession. What do you think by "getting kennel in your base" ?