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
If you drop a quetzal due to knockout, and it lands next to a giga...just know, the quetzal belong to the giga. Now you get to watch your would be quetzal get eaten by a giga. Now you can go home and cry.
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.