I wouldn't treat the QT, cause now you have to up your dose in comparision to the stregnth of the dosage. Plus after treatment, you'd have to do a water change and if you have a larger QT like a 20gal or so you would have to do WC's, use carbon to soak up extra meds etc.... IF you treat in a bucket, your just using 2 gallons, ( 1 gal for each bucket ), and toss water once completed. I use TANK water btw. this gives me an excuse to do my water change, use the water I'm going to throw out anyways as my dip water with meds and my rinse water.
I'd just use the QT as a holding tank to let the frags heal in peace without being bothered / eaten by pods or other inverts, bothered by fish etc...