Just went through (finally) setting up QT cause I need to treat my fish with hypo. I had similar questions but it makes sense why that's not going to work. You need to have bacteria built up for the biological filtration aspect. Also, you'd still need to cycle the tank. Here's your quickest bet: take some sand and a piece of rock from your DT, as much water as you're safely able to, and cycle. You can use a raw cocktail shrimp if you really want to kick it off, but honestly, there's no way it'll be ready for fish tomorrow. Some of the ready made bacteria in a bottle might help, but you still need to get through the entire nitrogen cycle and get some bacteria buildup in order for it to successfully hold most fish (some fish are hardier and can go in right at the end of a cycle, some can't).
If you plan on doing hypo or treating before putting the fish in your DT, you need to take out any rock you put in the tank for cycling, but you should have something in there for bacteria to grow on. Some use PVC, others use cheap ornaments.
Hope that helps.