Is she doing this all the time? It's possible that she stuck her beak in some poo (mine did that ALOT) and is/was trying to clear it off. That's all I know, sorry for being useless.
I'm with Red&Yellow-this is a new one on me. I had a White Leghorn rooster that did a lot of head shaking, but that was due to his giant wattles.
Really odd, hope someone can help you.
I'm afraid it may be neurological. If she stretches her neck fully when she sleeps it seems to be less frequently. I have checked her eyes and nose no stuffy nose or gunky eyes.
I did a search and couldn't come up with anything definitive.
What I would do if I were you is change the title of your threat to something like 1 week old BO chick with head shake-might get you more attention and hopefully more help!
Good luck to you and I sure hope you get to the bottom of this.