So here is a story once on mobile I found one I am playing solo so I go and gear up for the tame it takes me from the swamp to the winter biome to the redwood to the north beach to the south beach back to the swamp I finally bring it down over the swamp instantly it gets attacked by a spino I am on a pterronadon I try to lead it away and I lost both my beloved pterronadon and the quezt so my tip be careful where you bring one down

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.

If you have any dodo arrows, make a trap (tutorials on YouTube) the shoot the quetzal with the dodo arrows. The quetzal will get triggered at you and lead it to the trap.

I always find my quetzals at the red obelisk