You can keep quail in cages, or pens as they are called. Those rabbit hutches work really well for a handful of birds. Even aviary style settings work for quail too.
You can keep them on wire or solid floors with bedding. They will need a shallow pan of dirt or sand for dust bathing. Quail need a diet high in protein so a gamebird food with 24% to 28% protein is what they need. For laying hens, provide crushed oyster shell on the side. Quail are seasonal layers, laying spring thru fall.
A few branches propped up in the corner of the pen gives them some privacy and security.
They also love the treats like greens, veggies, quartered apples or peaches, all manner of seeds and mealworms.
Quail need to be wormed once or twice a year.