Dragonhawk mounts are fairly uncommon. Though they hail from Quel'Thalas and are a frequent companion of blood elves, these mounts are evenly split across the two factions. Around half of them are rewards from collections achievements.
Dragonhawk mounts first became available with patch 3.0.8, although the dragonhawk models were already rideable as early as patch 2.0.1 and flight masters in Quel'Thalas were given dragonhawk taxis with patch 2.4.
The Amani Dragonhawk is redeemed from the Amani Dragonhawk loot card from the Twilight of the Dragons TCG set.
These mounts exist in the game's database but are currently not available: