Hello there and welcome to BYC!
I am sorry about your tiny baby!

What breed are they? Did you hatch these yourself? What is the temp under the heat lamp or electric hen? What is the set up inside your brooder? Did you dip beaks in the water at hatch? Did you grind the food down to near powder? Does your brooder have solid sides, open top? What material are you using as bedding? (Sand can kill babies if they eat it)
Sorry about all the questions, but quail are very delicate at hatch and can be hard to keep alive if you don't pay attention to every detail. They chill easily and should be started at around 95 degrees. Food must be crushed or they can't eat. Show them where the water and food is, tap at the food you have sprinked on the floor of the brooder around the feeder, as if you are eating it. No open sides on the brooder, the drafts coming in will kill them. Make sure they have enough space in that there is no competition for sustenance, along with cool spots in the brooder to cool off. Also, if you hatched these yourself using a pre used incubator, the machine needs to be thoroughly fumigated before a new hatch, or diseases are incubated as well, killing the babies the first week.
Give us a bit more detail on your set up and maybe we can get down to the bottom of this!
I hope this little one will be ok!