The Tiny Emerald Whelpling drops from Dreaming Whelps in the Swamp of Sorrows. Unlike the source of the other two pets, the Tiny Crimson Whelpling and Dark Whelpling, there are also Adolescent Whelps located here which do not drop the pet but must still be killed as they often take the spawn location of Dreaming Whelps. Due to this, it is generally considered to be the rarest and most valuable of the three pets as it requires more effort to kill the mobs that matter.
The drop rate of this pet is roughly 0.1% (one in every thousand kills) and takes an incredible amount of patience and determination in order to get one. Due to the difficulty of obtaining one, and thus their rarity, they can sell for fairly large amounts of gold on the Auction House, at least as far as pets are concerned.