I was poking Warcraft Pets and discovered that if you set up a log in, you can keep track of your pet collection!
You can view Mooire's pet collection here. I have pets on other characters, but chose to just keep up with only Mooire's as she's my main. I currently have 34 out of 76 pets that I can actually obtain. I have excluded the Murloc pets (not available on US servers), Lucky (Asian promo pet), Engineering BoP pets, the Alliance only quest pet, and the two collector's edition pets that Mooire doesn't have (had to pick 1 out of 3 options and the Panda won).
Out of the 42 remaining pets, I really only want 7 of them; Chuck, who will be in patch 2.4, Hyacinth Macaw, Peanut, Phoenix Hatchling (must have!!), Rocket Chicken, Smolderweb Hatchling, and Winter's Little Helper.
I really hope they put in the Pet Bag, because I need 2 of them!