I have some in the spare bedroom right now that are about a month old. I haven't had any escapees yet, and their brooder is not covered. Granted, there are only 3 of them, so that might make a difference! Plus they have been with chicks and keets the whole time, so maybe they figure the keets are spazzy enough for them all??
I would wait until they have a good amount of feathers, unless there is someway that you can put a heat light on them outside.
Oh, and I didn't realize they were so little, obviously I wouldn't move them now!
I mix pine pellets and shavings together for my birds' bedding, and this helps a lot with cleaning. I have 25 coturnix chicks, 6 keets, and a chicken chick in a brooder together. I cleaned their box out today for the first time, and they are over a week old. Come to find out, it was the baby goose's box that was stinky, the quails' could have went another week probably