Whay are you filling a shoebox with sand? For dustbathing? I would use Liriope or some other long type grass/ground cover. Quail like to hide in tall grasses and low brush..They seem to like it thick too..
They would eat the grass down to nothing and dust in the dirt. You might as well just pull weeds out of your yard and just give them a box of sand to play in. I would recommend a plastic or wood box though, cardboard would wear out pretty fast.