I understand the economy of using tank water and did that for a while but now use only new aged water for changes in qt for two reasons in this case:
Frist, the display is contaminated with ich and though the chances of moving in a cyst or theront lookin gfor a fish are small , I'd avoid them.
Second , tank water carries organics with it and not the bio filtering benthic bacteria to handle them. In short, tank water can contribute to ammonia production in an uncyled qt tank,ime.
The water in qt can be at lower sg and raised up to display tank levels over time . Match the sg and temp and you're good to go.
You can put some sponge material or othe surface material,bioballs, etc in the qt system to help ammonia oxidizing bacteria to get going. Seeding in some commercial bacterial supplement could acelerate the cycle. Using an ammonia detoxifier, like ammo lock or amquell for a couple of weeks is a high priority if there are no meds used in this holding tank. Monitor ammonia daily for the first two weeks by then a biofilter should be going if there is adequate surface area. Don't worry about nitrite or nitrate. Focus on ammonia.