I am relatively new to quails. It didn't even occur to me to put them off the ground so when we bought 5 quail chicks we put them in a large rabbit run and coop on the grass and we move them every few days for fresh grass and goodies to forage around for. They are so happy and they love rummaging for insects and things. We cover one end so that they can hide when they like (which is often). It's very low to the ground, but they never bash their heads on the wire because they have places to hide when they're scared.
When I first started looking into how quail are kept commercially, even on a small scale, in those raised wire cages with places for the eggs to roll, I was pretty horrified actually. These little, living birds love to run around, and they love to do what they're instinctively programmed to do, which is to forage. Ours seem pretty hardy - they love standing out in the rain. But when it gets much colder we'll move the run to a barn for the winter and give them wood chips to scratch around in on the floor.
None of this makes collecting eggs the easiest, but it only takes a few more minutes than it might for us, whereas a lot more happiness for the quails.