Running a new filter for a period of time on an established tank is a good idea, but there really isn't any reason to worry about setting up a new tank the same day. Your filters will be fine, and as long as you aren't adding a bunch of new fish at the same time you are setting up the new tank, the bioload on the filters is essentially the same in the new tank. Yes, you'll lose some of the capacity of the beneficial bacteria that are growing on the surface of things in the tank, but that is minimal compared to the colony that exists in the filters themselves. I also see no reason to save tank water from the old tank. The bacteria is on the surface of things in the tank, not in the water column. All you'd be doing by using old water is bringing over whatever waste is left over in the water.
When ever I set up a new tank, I simply take a filter off an established tank (I keep multiple air driven sponges in tanks for specifically this reason), put it in the new tank, and its good. I've done this on a dozen tanks, and never had any issues.
