Nah'qi flies counterclockwise around Amirdrassil, but very high up, just below the tree's canopy. She isn't flagged as a rare, so you won't see a rare marker on your map. Taming this unique owl requires a special skill which is taught by the Cinder of Companionship. The Cinder is awarded when you learn the mount item Reins of Anu'relos, Flame's Guidance which is a rare drop from Mythic Fyrakk in the Amirdrassil raid. Using the Cinder creates an account-wide unlock for you to tame Nah'qi, so you don't have to specifically obtain it on your hunter.
Level scaling: In Shadowlands most NPCs will scale with the Hunter's level, within the constraints of their level range. Hunters can tame regular NPCs up to 2 levels higher than them, but can only tame elite NPCs of the hunter's level or below.