This will be another post that I will update regularly as new reports come in. This will be a list of bosses that not only have the best chance to drop a pet, but regularly drop other nice, class specific gear as well so, even if you don't get your pet, you at least have something to show for your trouble.
Skull Island [Orchid Chameleon]
Fin Dorsal (Jonah Town, Gullet)
Cool Ranch [Armadillo Verde, Golden Stingtail, Tropical Skysnake]
Johnny Ringo (Cooper's Roost, Cool Ranch)
El Guapo (Banditoad Gulch, Santo Pollo)
Santa Rana (Santa Rana's Palace, Santo Pollo)
Duck of Death (Boot Hill, Cool Ranch)
Mooshu [Ebon Spectre, Tawny Turtle]
Kung Po (Tempest, Khotan Skyway)
Also, the White-Tailed Jackalope is awarded for completing the Frontier Drifter Badge in Cool Ranch, which you earn by visiting 21 important areas. If you do all the main story quest, you'll probably be close to getting this one.
I think there is a similar quest in Mooshu for a Celestial Dragon Pet, but I couldn't find the particulars.