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.
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.