Have your brooder ready so when the chicks hatch, you can transfer them quickly into a warm area. Be very careful when removing chicks from the incubator so you don't drop them. A brooder can be anything from a cardboard box, a plastic tote or even one of those round livestock watering troughs. Use only brooders that have a solid floor and 4 solid walls. No open brooding areas for Quail. Quail chicks are very susceptable to drafts and dying in the brooder so pay attention to detail when setting up their area. Never cram chicks in. It only leads to over heating, aggression, trampling, starving and or dying of thirst due to too much competition. So start with giving them about 1/2 square foot per chick in the brooder. As they grow, depending on the breed and their size, you may need to increase this size to 1 square foot at 3 weeks of age. (You will need to follow this space requirement for all chicks in the New World Quail grouping.)
For bedding, you can use pine shavings, (never use cedar shavings...toxic on the lungs) grass hay or even raise them on wire. I raise all my chicks on wire...1/4 inch to start and then 1/2 inch by 2 or 3 weeks of age. Wire is very sanitary for the chicks. Babies are pooping machines and the poop also carries Coccidiosis which Quail chicks are very susceptable too. Cocci kills. You can lose entire batches of Quail due to cocci. If you do not use wire, keep your brooder EXTREMELY clean! If you are finding soiled feed and water, keep water and feed elevated after they are large enough to reach, keep it clean and remove all wet bedding daily.
Baby Quail are extremely tiny at hatch, ranging from as small as a button and on up to the size of a bumble bee and can drown very easily in their water. So you will want to use either a chick waterer with tiny stones...
or use a regular water font with tiny stones or marbles in the base. And this is especially important if you are hatching Button Quail. If you only have a couple chicks, the lid of a jelly jar with tiny stones in it works well too. Just something to keep them from falling in as they can and do. When transferring your chicks to the brooder, individually dip each beak in the water. Quail need to drink immediately after hatch. Set them down right in front of the water so they will keep drinking. This also helps to prevent pasty butt. Eating before drinking after hatch leads to pasty butt through dehydration. So make SURE they all get a good drink of water before eating. If you have to, dip the beaks again later that day to make sure they all know where the water is.
You will want to lay paper towels down over your bedding for the first week and sprinkle CRUSHED gamebird chick starter all around the feeder area on these towels so they can find the feed. Do not be tempted to use chicken chick starter as it does not have enough protein for growing Quail babies and can cause all kinds if growth and health issues. Once you know they all know where the feed is stored, you can removed the towels, usually after 3 days or so. You can stop crushing the feed after 1 to 2 weeks depending on which breed and size you are raising. Quail chicks are too tiny to eat the crumbles right out of the bag. It doesn't have to be powder, but make sure it is small enough for them to eat or they will starve to death. You will need to tap with your fingers at the food throughout that first day to help them find the food. Quail are just not that smart at hatch.
As for heat and lighting...I recommend using an Infra-red bulb (not to be confused with the standard red bulb). Infra-red will allow for a normal sleeping pattern at night and keeps Quail mentally chilled. It is also a very penetrable light warming them internally. Bobwhites are notorious for killing each other in the brooder so never use a white light on Bobs. White lighting is too excitable and if they are not sleeping, you will have little killing monsters on your hands. White lighting can burn the surface but leave the internal tissue cold. So infra-red only. Red bulb if you can't find infra-red. Lay a good thermometer on the floor directly beneath the heat source. Heat on one side of the brooder, food and water on the other. This will allow for cool spots in the brooder. Chicks can't yet regulate their internal temps and can over heat or chill very easily. So give them places to cool off. Start the heat off at 95 to 97 degrees Fahrenheit. (The New World birds like it a bit higher than 95.) Make SURE your thermometer is reading correctly as even a few degrees off in either direction and you can kill your chicks. You are going to lower the temp by 5 degrees each week until they are fully feathered or 5 to 6 weeks. If at any time you start to see aggression in the brooder, you either have them crammed in and or it is way too warm for them. Give them more space if they need it and lower the temp by 3 or 4 degrees. Then you will work your heat down from there each week. Heat/light is left on 24/7 until they are ready to head outside to their new living quarters.
You can also give them things to do in the brooder too. It can get mighty boring in there at times. After a few days or so I like to put some cut branches from outside to give them places to climb on, and a low box with some sand, alfalfa leaves and chick starter in it gives them a place to scratch around in. They also might appreciate some small mirrors or parrot toys. Just make sure there is nothing that they can swallow on these toys.
Change the water daily and keep the feeder topped off and clean. Keep the brooder as clean as possible at all times.
Lastly, do NOT cover your brooder with anything but a screen or wire. You want good heat and oxygen exchange out the top of the brooder. A screen also helps protect them should the light fall into the brooder.
At 5 to 6 weeks, they are now ready to head outside to their living area. They will not be mature for breeding until next spring at which time they will require 4 square feet per bird and be paired off, one male to one female. Pairs need to be kept separate from each other during the breeding season of spring through fall as they can kill each other. From fall through to spring, they enjoy being rejoined together to covey up for winter. Bobs mate for life with one female so try to keep the pairs straight.