If you got a big brain like some youtubers use a tapejara or a griffin since you can whistle agro on a quetz in the passenger seat. Then get dem tranqs are start shooting it tell its nocked. If its in a dangerous area put metal or wood spikes around it deppending on the area.
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.
In order to solo tame a quetz, you could use an argentavis and a pulmiscorpius. Just pick up the pulmiscorpius, and do whistle attack target while looking at the quetz, your pulmiscorpius should start attacking the quetz, raising it's torpidity until it is knocked out.