Button quail are tiny, and hence don't need much of a brooder.
I had 20 eggs mailed, 10 of them actually hatched out.
For a brooder I am using a 10 gal tank with shelf liner on the floor for footing to prevent splayed legs. 3 sides of the tank covered with coroplast for insulation and for more feeling of security. heat source is a 60 watt bulb in a clamp lamp controlled by a lamp dimmer. 2 bricks standing on one end of the tank with the lamp resting on them., The bricks warm up from the lamp heat and the chicks can huddle next to the bricks for warmth in addition to the actual lamp heat.
for water, I am using a quail chick mason jar waterer with marbles in it to keep them from drowning or getting too wet.
Not my pic but this is where I got the info:

http://ncws.com/mcdonald/CareFeed.htm