Dragonhawk Hatchlings
The easiest type of noncombat pets to obtain for blood elves are dragonhawk hatchlings. These pets are available in three different colors, gold, silver and red. You can purchase them from Jilanne, a vendor found at Fairbreeze Village in Eversong Woods, for 50 silver each. A fourth color of dragonhawk hatchling, blue, is only sold by a vendor found in the Netherstorm area, and is therefore much harder to get.
Other Noncombat Pets
Vendors who sell noncombat pets also exist in Orgrimmar, Thunder Bluff and Undercity. Jeremiah Payson, found near the bank in Undercity, sells a cockroach pet, while Halpa, found near the middle of Thunder Bluff, sells a prairie dog pet. Xan'tish, found in the Valley of Spirits in Orgrimmar, sells three different colors of snakes, brown, red and black. All of these pets cost 50 silver each. Several other types of vanity pets also exist. You may be able to purchase some from the auction house or directly from other players, buy them from vendors around the world or obtain them as loot from enemies you kill.
Dragonhawk Hunter Pet
All blood-elf hunters begin the game with a dragonhawk pet. Although you can't control the pet's actions directly until you reach level 10, it will attack the enemy you are attacking and help you defeat it. Once you reach level 20, your dragonhawk pet will start gaining talent points every four levels. You can invest these talent points to improve its damage or teach it new abilities.
Other Hunter Pets
Once you reach level 10, you can learn how to tame different types of beast to be your pet. Whether you can tame a specific beast or not depends on your level: you must be equal or higher in level than the beast you want to tame. Several beasts in Eversong Woods, the starting zone for blood elves, can be tamed. You can find a dragonhawk with slightly different colors than the one you started the game with, brown and red lynxes, a bronze crab and a green turtle.