Thanks for the advice all.  I don't have poly-vi-sol, but I did pick up some bird vitamins 'for small birds'- it was all I could find.  Do you think it's okay for a chick?  I can go to the supermarket and get the baby vitamins.  (Wish I'd read the posts mentioning it before I went and hunted down the other stuff.)
Anyway, I'm happy to report that the peep has improved drastically today.  She still has the head bobbing, but it seems only to happen when she is really active.  This leads me to believe that it is, in fact, occurring with each breath and maybe not a neurological thing.  Either way, when rested, the movement is hardly noticable, if there at all.  I brought her and a few of the other peeps out of the brooders and placed them in the floor with a bowl of food and water.   After watching the other peeps eat, she followed suit.  I was hoping that the 'monkey see, monkey do' thing would work- and it did.  YAY!
I then decided to put her in to the large brooder for a bit and see how she did.  Dummy me sprayed her feet with blue-kote so that I would be able to tell her from the rest and all that ended up doing was to make the other peeps want to peck at her toes...so, she's back in her hospital brooder, but with just one peep to keep her company.  (How long does it take for blue-kote to wear off?)
I noticed a bit of peculiar behavior from her when I had put her back in the large brooder- she seemed to really want to snuggle in under the other peeps wings.  She does this with my hands when I hold her, too.  I don't know what to make of it.
Hopefully she will continue to get better.  I sure wish I knew what disease/illness/whatever this is that we are dealing with.