It's kind of a "catch 22" question. If you use the same filter in the "q" tank all the time you risk introducing something the last batch of fish in the "q" tank might have had to the next batch.
On the other hand, you run the same risk by taking a filter from an existing tank and using it in the "q" tank. You may be introducing something from the existing tank to the new batch of fish in the "q" tank.
I don't know if there's a good way to "disinfect" a sponge filter of any "nasties" but not kill the good bacteria.
Personally I think if the fish in the "q" tank didn't show any signs of any problems I would reuse that same sponge. I would squeeze it out well and then add straight ammonia to the water every day or so to re-establish the good bacteria and then to also keep it going.
GARY