Yes, it should work totally fine to move the chicks out together as soon as the coop is secure, I'd move them at the same time right before dark.
Beware that 6 weeks, for many breeds, will often be too old for brooder space... one day you walk up to them and they've exploded like popcorn in...
What @rosemarythyme said :)
This year I have a lot of small batches of chicks coming out of the incubators, so we're often integrating different ages. I find it goes best if the youngest are really confident in this life stuff before mixing them with chicks older than a week.
I also take...