I didn't know this when I first started taming or playing the game but if you knock out the quetzal (or any wild flying type in general) and they fall from a great night they won't take any damage. But it is a good idea to plant spikes in a half circle (if low on resources) you can guard the enter and exit spot to access it's inventory and guard it's sides from other hostile wilds without being right there. Happy taming, yes use kibble!
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.