I think they should implement Epic.
If i had designed this, I would have made anything "easily" obtainable common. That would be anything an in game vendor sells, as well as the online store. Uncommon would apply to all quest pets. That would include the Darkmoon pets. Rare would apply to all the drop pets, except for specific ones.
those specific exceptions would be the extremely hard to get drops. Such as the Hyacinth Macaw, or Black Tabby Cat, Azure Whelpling, Tiny Emerald Whelpling. You get the idea. The current "rare" pets would be bumped up to Epic status, along with the no longer available pets, like the Spirit of Competition, Baby Blizzard bear, Vampiric Batling.
Holiday pets would be an issue. I would have called them rare, but the Sinister Squashling has become sadly common. So I would probably mark those as uncommon. They are still once a year things.
Trading Card pets would be common.
Collector's edition pets would be rare, as well as pets obtained through purchase of other blizzard games, and Blizzcon pets.
The corehound would be uncommon.
Achievement pets would be Epic.
and as far as the wild pets go, i kind of like the way it is. My only issue there is the trapping part, which is not the topic of this thread. And certain spiders. They should not be able to kill themselves with their attack. I lost three potential rares that way. Sorry, running off topic there.
did i miss any pets? Oh! Fishing pets! NOT the four crocs from the dailies, those would be considered quest pets, and therefore uncommon. However the Magical Crawdad, Seapony, and anything else you actually have to fish out of the water would be considered epic. yes i know that those pets are not as difficult to obtain as say the Emerald whelpling, but you do need flight and high leveled fishing to obtain the crawdad, and just as much patience as a whelpling farmer to fish them up.
I'm quite sure my ideas are not perfect, and would certainly not be welcomed by certain pet owners. I think this is a fairly effecient way to classify the non wild pets. Though I'm sure any flaws will be pointed out, and in fact welcomed. Fresh perspective is always good.