So they are babies. Wasn't sure with your first post.
Your "must haves" included a brooder/coop of some sort that is predator safe and gives them protection from the environment. The environment means no rain or direct wind hitting them. They need a warm spot to go to so they can warm up if they need to but too much heat is dangerous. To me the ideal is one spot warm enough in the coolest conditions and a spot cool enough in the warmest conditions. I find chicks straight out of the incubator are capable of moving to safe areas of heat as long as they have the option. People use all kinds of ways to provide that warm spot. I use heat lamps but heat plates, heating pads, emitters, and various other heating devices work. What do you use for your quail? It should work.
You need food and water. The food should be low-calcium and of relatively high protein content. Typically 18% to 20% protein is used with calcium content in the 1% range, but some people use game bird feed with a protein content up to 24%. Just watch the calcium.
There are all kinds of things you can use or even make for feeders and waterers. I've made shallow troughs out of scrap wood to use as feeders. You can buy various things. You just want the feed where they can get to it. I haven't done quail but I'd think their behaviors would really be similar.
I don't know how you water your quail. The chicks will grow pretty fast but to start with they aren't that big. Again you can buy or use different things to use as waterers. Some people use nipple systems, some use a jar with a vacuum fed lid. I use this, just fill it with rocks so the chicks can walk on it without drowning and an drink between the rocks. This photo is for older chickens that aren't in danger of drowning. Keep the water clean. Dirty water is dangerous.
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Like all birds they need decent ventilation.
The brooder needs to stay dry. A wet brooder is a dangerous brooder pus it can stink. I brood over wire but there are many different beddings you can use to absorb moisture. Try to avoid spilled water and change bedding as required. Their poop can build up and remain wet.
Size. You need room for food, water, and for them to grow. How much room depends on what age you move them out. You can move them to a larger brooder if you need to. I'm not into magic numbers of square feet per chick as it depends on various things. If they start to look crowded, they are.
An easy quick way to make a brooder is to use a large cardboard box. You can maybe get a large appliance box or tape a couple of boxes together. Tape on another box if it needs to grow. Put something on the garage floor like plywood or cardboard to protect the floor from staining and use bedding like wood shavings, straw, crushed dried leaves, maybe even shredded paper.
They will soon learn to fly. I've had some two weeks old fly over three feet with little effort. So think how you might fix a lid on that to stop them from flying out. A light frame with wire mesh on it can be pretty easy to make.
There are no hard and fast rules on how you have to do any of this. If you have your coop finished and electricity out there for heat you can move the to the coop at any time. No need to make it really complicated or expensive. Predator and environmental protection. A warm spot and a cool spot. Ventilation. Food. Water. A dry brooder. How you go about any of this doesn't matter that much. Your quail experience should help.
