Good news is that there's a script that you can macro that will list what the qualities are of the pets you're currently battling against! Check it out here, or see below.
/run for i=1,C_PetBattles.GetNumPets(2) do SELECTED_CHAT_FRAME:AddMessage(C_PetBattles.GetName(2,i).." - ".._G["BATTLE_PET_BREED_QUALITY"..C_PetBattles.GetBreedQuality(2,i)]) endJust copy and paste the above into a macro and place it onto your action bars. After that, simply enter a Pet Battle and use the macro.
Since the Pet Battles UI overrides your normal UI, you'll need to keybind the macro to something other than the numbers 1-6. Although you can't see the macro when in combat, if you hit its assigned keybind as soon as you enter a Pet Battle, you'll be able to see each pet's quality status in your chat window.
Note: If you're not copying and pasting and choose to type it out instead, there are no line breaks in the above script.
I didn't mention this sooner because I wasn't sure if Blizzard would consider this an exploit or not. But since there's even a Wowinsider article on it, I figured I'd help spread the info. Makes it a little easier on everyone! :)