Having a disinfected QT is more important than a cycled one. You have to start with a clean slate. I clean my QTs between sessions with a bleach solution to ensure nothing icky can infect the fish. I match the QT's salinity to the incoming bagged fish's water, so I can float and release, saving the fish a ton of stress. If the fish shows symptoms, I begin appropriate meds asap. If its ICH, I start lowering salinity to hypo salinity, rather than using copper. Then I use ammonia test strips to monitor water and do water changes when needed. If its not ICH, but something else, I'll do hypo AFTER the treatment.
In a one month-ish QT session, you may not see ammonia levels rise before its over. In the past, I kept my QTs up and running, and likely infected the incoming fish from the start!
Once your display tank is up and running, and cycled, you can scoop a spoonful of sand from it and add it to your QT. I also throw a pruned piece of macro algae in there to help suck up nutrients and make the QT more homey.
Good luck with your build!