Solo knockout - You need an Argentavis - (Preferably a decent level) Step 1. Grapple hook onto the Argentavis. Then, shoot it with your tranquilizer darts or arrows, until it flies too far away. Step 3. Whistle your Argentavis to aggressive and then passive before it attacks the quetzal. Repeat the process until it goes down. Step 4. Use the information from DodoDex to tame the creature when it's down. I recommend putting spike walls around it to protect it when it's down. A chair and some war drums are also a good addition, but not mandatory.
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.