This may sound like an odd question, but do you use white or red bulbs for their heat source?
I've found that red light almost always prevents picking, because a white light will show if someone's managed to start a new feather bleeding, and birds will pick at red blood; with red bulbs, it hides the blood color, and the other chicks don't all gang up on the bleeding chick.
It sounds like it wouldn't be a diet deficiency, but it never hurts to mix in some vitamin/electrolyte mix like what Durvet sells into their water ever so often. I do that with the first week's water for a new hatch, anyway, just to get them going on the right foot.
As long as there's no significant injuries to the other chicks, there shouldn't be much danger. But be sure to cover any injured areas with blu-kote. It also hides blood, as well as being a great help to healing and keeping infection away.
Quail, like other birds, don't do well alone. You might start by introducing another baby into the area with the "picker" and see what happens.