Hi, welcome to BYC!
I have 13 king (button) quails, one is just a chick. I keep mine outside in rabbit hutches or parrot breeding cages as these are a good size for a pair of quails. I know a lot of people keep them inside in fish tank setups because it gets cold outside but I'm in Australia where it doesn't really get cold so they do fine outside (king quails are actually native to Australia). If it gets cold where you live, I would keep them inside in a fish tank. The space requirement is 1 square foot per bird, you can do more than this, I try to.
For a brooder, I use a fish tank with a heat lamp and put paper towel on the bottom for the first few days to a week as it's an even surface and you can monitor eating better. I then put straw in the bottom when they're older as it is easier to keep clean as you don't need to change it every hour! Make sure you have shallow water dishes because if they can drown, they will drown. For feed for the chicks, I use game bird starter with 28% protein (it doesn't have to be 28%, that's all that's available to me, they still need high protein though) until they are 6-8 weeks old, then I move to game bird finisher with 22% protein.
Quails are ground dwelling birds who need more ground space, however, if startled, they will fly, I've had two kings fly away, now my hutches are in aviaries for extra security.
They do like baths as in dust baths with dirt or sand where they'll roll around, on hot days, mine try to bathe in their water dishes though it's generally not a good idea to get them too wet as they can get sick.
Here is what I use for my adult water dishes.
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And here's some cute pictures of mama quail with her babies, it's important for research
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Hope I've answered some of your questions, if you want to know anything else, feel free to ask, we're happy to help!