I've never kept quail, but with my bantam chicks (and with any of my chicks) I usually put them on a sheet or paper towels for the first week or two, sometimes longer. This allows me to see what their droppings look like, as well as allowing them to have something that is easy to grip with their feet and that they can't eat. After they get stronger you can switch to shavings.
Do NOT use shavings for baby quail! They can eat them by accident, get them stuck in their throats, and it is hard to see their droppings on the shavings. Use a mat, towel, or small piece of carpet on the bottom of the cage.
Not that you can't but it really is better to just use a skid free surface for at least the first few days. You will save yourself a bunch of headaches. After a few days sand can be used or small wire. After a couple weeks wire is best.
I bought a roll of the rubber shelf liner that is perforated at Wally World. Cut several sheets to cover part of my brooder. Worked great, after a couple of days pull em out and put clean in and wash the dirty ones and let dry repeat.
After 2 weeks I put some wood shavings in too, however they were hard to keep clean and change out. Won't do that again have large bag for sale cheap LOL.
I found that puppy piddle pads work awesome the first week. More absorbent than paper towels and easier to change. I just get the large ones so it only takes one to line the bottom on the brooder. I discovered using them by accident when I ran out of paper towels and it was all I had to use ( my dogs use them when I go to work)