I hand raised all of my quail, from Coturnix, to Bobwhites to Buttons! Hand raised Coturnix were WAY friendlier than the parent stock I'd bought (which I assume weren't hand raised.) The friendlies quail I'd raised was accidental hatch (6 in the incubator, 1 hatched) so she was for the most part alone and she was very human friendly as you can expect as she was my best friend for a month until our Bobwhites and other Coturnix hatched : D she stayed very friendly even once she became part of the flock of other not-as-friendly-but-still-handraised quail! I'd let her out of the hutch while I was cleaning, feeding, just walking by, Frankie would follow my feet, sit on top of my feet, dust bathe in and next to me while I did chores. She was the best quail I could have ever asked for. Now I'm not sure if recommend doing it. Raising a solo ANYTHING is not a good idea (except maybe humans but I don't know much about that species, haven't raised any and I was also an only haha ;D) I'd get a few chicks and hand raise them and cross your fingers! Even then you still may get one/some who aren't super friendly.
Also I get that it's not poultry, but some of the best not-dog/cat/horse therapy animals I've seen were rabbits <3 they're fairly easy to care for too! I won't bla bla on about rabbits though since you're looking into quail but I just wanted to mention them <3 chickens also make lovely therapy animals! Out of my own flock I'd choose a bantam cochin or an OEGB (and our bantam leghorn is great but she's really different from MANY other leghorns, bantam or not I've seen!)