Why are you going to go through this for a QT tank... IMHO it is overkill. All you need is a heater, a powerhead or two, and if it is fish only, a NO light and maybe some sort of sponge filter for biological filtration. Would be nice to put some different sized PVC pipe in there to give the fish some place to hide and feel save. I use a peguin mini filter on the back just cuz I had one laying around.
The reason that is all you want in there is you SHOULD set up and tear down your QT after every use. You should clean it out between uses and store it till needed. It would be best to throw out your biological filtration and use a "new" sponge filter the next time you QT something. You can store your "new" sponge filter in your tank a week or so prior to hen you know you are going to QT and it will be seeded with bacteria. I keep one in my tank at all times and when I use that one I pop a new one in there. It could be months till I need it again but it just sits in my sump.
To answer your original question, it should take a week or two for your bioballs to be good an seeded if that is what you decide to use.