Not found any post like this, or I just search bad.
I was bored powerleveling so I gathered information based on my own fights, using the rarity-addon, which you can find here http://www.wowinterface.com/downloads/info21340-PetBattleRarity.html#info
I did these fights in three zones. Terokkar Forest, Kun-Lai Summit and Valley of Blossom (the alliance city zone) or what it's called. Generally didn't feel like the ratings were diffrent in other zones.
I know it's not much info to make accurate stats out of, but at least it gives a few hints.
It seems like it's static 35% chance for poor, 30% on common and uncommon and 5% for rare, for the "main" pet.
And it feels like it's higher chance for poor on 2'nd and 3'rd pet, just to make the fights a bit easier.
Will keep putting down numbers when servers are working again.
This first one is based on 100 fights (easy to count!), and only based on the actual pet you see on map (first one you battle).
This second one is based on 87 fights, and it's based on all three pets (261) in every fight and their rarity. I started this 13 fights after above one.