Now that you have use copper in the main display,you will not be able to keep any inverts including shrimps,crabs,snails etc.If at any time in the future you want to add live rock,the copper will kill copepods,worms and mini brittlestars that hitchhike with live rock too.My suggestion is to drain the system,throw away the substrate and clean the tank thoroughly.In other words,start over.
A tank will cycle without live rock and sand.It can take much longer than using live rock.Also there needs to be some kind of waste(fish food,raw table shrimp,live fish-not recommended)to jump start the cycle.Seriously,even just fish keepers have live rock these days,I highly recommend it.
You can use a sponge filter that has been ran in the sump or display for several weeks.The beneficial bacteria will colonize the filter to be use in a quarantine tank.That is if you are using it strictly for quarantining fish.If you are using the QT to treat for illness than there is no point in putting in the sponge filter.Use water from the display before adding them to the QT,then treat them.