One thing I have done is, if using HOB filters, to buy filters that use the same size meduim and when setting up a fry/quarantine/hospital tank you can simply move a filter pad from the mature tank to the 'back-up' filter on the other tank.
Or buy a small HOB flter or sponge filter and leave it running all the time on your main tank to make sure it's mature and move it to the fry-tank when it comes time. I find a small sponge filter works best for this.