It will take a few weeks for the biowheel to become coated with the beneficial bacteria. There is almost no bacteria in the water column so using old water from the DT tank does nothing and just brings dirty water over to the QT.
When you say you added fresh water, did you add any salt mix to bring it to the same SG
as the DT?
If you don't prepare for some water changes quickly things will do downhill fast. The fish will eat, what it can, then the rest and the fish poop will breakdown to ammonia and kill the fish. The only way to prevent that is to make the partial water changes until the new filter can be colonized by enough bacteria to offset the waste breakdown in the QT tank. Does that make sense?