If you are struggling to solo tame your first Quetz, just wait for v.248. In this update, we'll be able to equip weapons while mounted. If we can equip a rifle or crossbow with tranq darts or tranq arrows, this KO will be simple provided you have a decent stamina Ptero or Argent.
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.