Build a platform on another quetz.. use 4 stone foundations then add ceilings to them.. on the top add 3 dino gates without the doors but don't clip them together.. keep an extra in your inventory for when you catch a quetz so you place it to keep the quetz in place and it will stay on the platform after it is knocked out and you can tame it in the sky.. add a ramp at the front to make it easier to get up the back but make sure you have ceilings going right around to the front so you won't fall off
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.