Hello there and welcome to BYC! They don't need a run, but they do enjoy as much space as you can afford. And going outside into a run, dust bathing in the dirt, are all favorite things to do for a quail. However yes, you can just keep them in a hutch as long as they have enough space per bird. And I like to add fake or real foliage to a hutch to give it a more natural feeling. Quail LOVE to hang out under brush and such, it gives them privacy from the others and gives them a sense of protection. Also keeps them from flushing up into the ceiling. I use grass hay in my hutches too, easy to clean and keeps them off wire.
Coturnix Quail? You can easily keep about 15 birds in this space. Make sure to keep only all hens or only 1 male with hens in this space. 2 males probably wont work here.
Yes I want to eventually breed. So I'll probably also have a male too. What happens once I have chicks and there is a male(s) in that other than the first male?
I wouldn't build one that deep Unless you have really long arms. I build all of mine 24" deep by 10 ft and 10" tall. Figure 1 bird per sq. foot and they will have plenty of room. If you are going to breed quail later I would divide your cage into 3 or 4 compartments.
1 square foot is a square that is 1 foot deep and 1 foot across. 2 square feet is the same, 2 feet across, 2 feet deep. Quail generally dont go broody, so you will need an incubator. Chicks will need to be mature to mix into an adult flock. Do this slowly with a divider in the hutch, everybody sees, nobody touches for a couple weeks, then you can mix them.
So one bird to one square foot. And thanks @twocrows I was trying to figure out how to put chicks into the bigger flock