I'm very serious when I say that the Q tank should be very clean. If you have to keep moving the Q-shoal from the Q tank to another tank, you run the risk of them passing on diseases from the previous Q tank occupant or picking up diseases from other tanks. Plus, it means you're not in a position to throw away the media after it is used in the Q tank and the media can potentially harbor diseases.
What I do is always have some spare media in a main tank filter, and move that media over to the Q tank when I need it (if I use a filter at all, which I rarely do as many treatments kill filter bacteria anyway). I then replace that piece of media with new media in the main tank filter to ensure I always have fresh media avaliable. I then throw away the Q media after it is used.
I know what it's like to have something creeping around my tanks, killing off my fish. Something that was probably passed between tanks by mixing media or using the same net in multiple tanks. I learnt the hard way to be uber careful and while I'm not perfect by any means (cloned a new filter with mature media recently, for example), I do think it is important to be sure the Q tank is as sterile at possible, and that would mean not keeping fish in it between uses.