This solo knock out strategy is better than the grapple hook ones. So, all you need is:
-A Tapejara with a saddle
-Crossbow or Gun with tranq arrows/darts
-And of course taming food
-Just in case, bring some parachutes
So, after locating your Quetz, board the front seat of the Tapejara (passenger) and whistle 'attack this target' on the Quetzal. If it's too far, whistle attack on other creatures until it's airborne. When it is, whistle "move here" in the air, so you can follow the Quetzal without harming it. While you chase it you can tranq it down with AIMING! And you can control your Tapejara easily. Boom.
The fun way is to jump off and grapple to your argie and whistle it to attack and since argies are slow it won’t catch up in time so tranq till it goes out also bring parachutes and consider liking so more people will know
Put the honey in your hotbar (unstack them, so 1 in each slot)
Fly over him en throw the first honey on it’s body (press the hotkey from the honey and it will throw the honey) It will follow the honey that’s falling. Dino’s on the ground will eat the honey too so keep dropping honey until the quetzal is on the ground eating honey.
Place some dinosaur gates on top of him to get him stuck. Shoot it with tranq arrows and feed some prime meat
If you manage to knock a quetzal out, try starve taming. If you never tried starve taming it’s just leaving a Dino’s hunger go to half way or lower and then you start feeding. I’ve done this many times and it’s very useful taming trick.