I think in some cases like the fawn the ammount of poor to uncommon types outweighs the those of other pet's I've seen this with Darter Hatchlings, Bat's, the Lost of Lordoran and a few of the Moth species. Roaches on the other hand I've seen more Rare's than uncommons and nothing under common.
Not sure if it's RNG at work but I'll see if I can put together a list of type percentage if Bre would like.
Tonight I found about 8 rare fawns and 4 or 5 rare rabbits in about 45m outside Stormwind where everyone duels. It was crazy. And some of the pets were even getting killed by the aoe from the duelers. I've never seen so many pets respawn so fast and so many rares. Anyone having issues with fawns might want to check there!
And I found my rare #5 rabbit!! Elmo's gettin' an upgrade!
The fawn took me awhile to get as well but with a little patience you will get it. If you're interested in knowing rarity before capturing to save time go get the mod "Battle pet quality notifier" from curse. It tells you all pets rarity at the start of battle and will tell you upon mouseover of a wild pet whether you have it and what rarity and lvl it is. It should tide you over until 5.1 when blizz adds these features into the game.