The question is whether the variant thought is because the developers used the same model for a new creature to save time or whether they designed multiple creatures as part of a *species* range and each one you get is a different pet in that species.
The only function I can see that may help you see if that's possible is this one:
https://warcraft.wiki.gg/wiki/API_C_...PetInfoByIndex
petID, speciesID, owned, customName, level, favorite, isRevoked, speciesName, icon, petType, companionID, tooltip, description, isWild, canBattle, isTradeable, isUnique, obtainable = C_PetJournal.GetPetInfoByIndex(index)
index being the position in the journal starting from 1.
This is also an interesting function if it isn't linked to setting which pets are part of the random summon option. Could this mean that pets in some species have a random visual display explaining that *rarity* version you are talking about.
https://warcraft.wiki.gg/wiki/API_C_...sRandomDisplay
usesRandomDisplay = C_PetJournal.PetUsesRandomDisplay(speciesID)
The random summon function
https://warcraft.wiki.gg/wiki/API_C_...ummonRandomPet
C_PetJournal.SummonRandomPet(favoritePets)
This page just shows the option of only summoning a random pet amongst your favourites or all pets
But to help at the auction house. I doubt there is anything out there. There is no drop rate mentioned on any of the pets info so that drop rate is probably calculated outside of wow by the player base based on statistics. If not, where is that 0.02% drop rate accessed in game ?