Oh yes, they also should have some 'scenery', like fake (or real) plants, something for them to hide in. I have some critter cottages for mine, they are little grass huts basically. They always lay their eggs in there, and I've even had some that went broody on me. If they have plenty of room (3x4 is HUGE for 3 buttons!) and have plenty of things to hide in, under, or around, they could possibly brood for you! Just make sure the wire is no bigger than 1/2", cause even the adults can get through 1" wire. But they don't like to be chilled, that's why it's best for them to not be on the ground. If they get wet, they chill very easily. I normally keep mine covered on rainy days, since there is always a chill in the air.
And the bib is not a sure-fire way of sexing, some females can have that too. The only 'almost fool-proof' way to sex them is that only males (normally) have red/rust/pink colored feathers on their vents. But not all males do, so it's kind of tricky. Mostly colors like white, splash, and pied don't, but some silvers don't either.
ETA: But remember they are ground-dwellers, so they don't need much height. They like to hide when they lay eggs, my little houses are just tall enough for them to walk in without hitting their heads. It makes them feel safe to be hidden.
