Quail chicks need a LOT of room. More room in the brooder than chicken chicks. Quail babies can be cannibalistic and will pick at each others faces, toes, beaks and what ever else they can pick at. So it sounds to me that they are killing each other.
So the first thing I would suggest is to get a bigger brooder, or separate them into two brooders or if you can figure out who is the instigator in the group to start the pecking, separate that bird.
Next lower the temp in the brooder, no matter what week you are on. They will pick at each other if they are too warm. So right now, lower the time 5 degrees. If they get cold, they can huddle together to keep warm.
Next, give them something to do. Quail chicks get bored and will pick on each other. Put some cut branches in the brooder, with the leaves and stems so they can pick at those instead. Also, you can get a cereal box, lay it on it's side and cut one side off and the smaller side so they can climb in. Put in dirt, sand, grit, what ever you have, throw in some starter feed. Even leaves would work. Just give them something to occupy themselves.
May I ask what kind of quail? Bobwhites are the worst at getting along with each other, and it only gets worse as they get older! Good luck!