If you take the egg from the female Quetzal it will agro to you and try to hunt you down. For the trap you will need a couple large bear traps then some Dino gateways then you have it trap and you can tame it.
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.