Depends on what breed. Bobwhites...A pair. Coturnix....20 or so if you don't need more than one rooster. You can run multiple roos in coturnix pens but it doesn't work well in hobby sized cages (anything less than a couple hundred square feet).
The only issue I see is the top needs to be lined with something "soft" so they don't break their skulls if they flush. Anything over 12 inches needs to have something to slow or cushion the impact if one of the quail panics and jumps.