Different qualities aren't limited only to wild pets—many rare World drops and special non-wild companions have had their stats boosted. For example, the world-drop dragon whelps (Azure Whelpling, Crimson Whelpling, Dark Whelpling, and Emerald Whelpling) are of [rare] quality. Check your Pet Journal to see the color-coded rarity of your non-wild pets.
Thanks for stopping by! I'm Crzypck, officer, Raid Leader, and tank of Mist on Area 52, and the official raid guide writer partnered with Limit, the US#1 and World #2 guild. This is the home page for Limit's Official Battle of Dazar'alor Mythic Raid Guide. Every strategy guide has been thoroughly discussed, reviewed, and approved by officers from Limit.