We'll presume you are correct and she is really a she.
So she would be about 11 months old...that would mean she hatched last February?
Hmmmm....she should be laying by now. Ameraucanas/EE's mature more slowly than others, but generally lay by 6 to 8 months of age. That should have put her at maturity during summer with plenty of daylight, so it shouldn't be an issue of hitting maturity at the late fall when days are shortening...in those cases i often don't see young pullets of my slower maturing breeds come into lay until spring time.
My other thought would be...are you sure she isn't laying and hiding her eggs? I've had "late layers" end up laying everywhere but the nest box. I'd go on an easter egg hunt to see if maybe she is hiding her eggs in an unusual place. Watch her to see where she might be lingering.
The last thought is she is laying and you simply don't recognize her eggs as they are not blue. If she is an EE, rather than a true Ameraucana, she may lay brown or even white, instead of the trademark blue or green. Her eggs may be getting lost in the nest with the rest.
If none of that pans out, and you are absolutely sure she is a she, it is likely something is amiss with either her hormones or her egg duct, which would be genetic...it could be calcium deficiency or possibly worm load...general health would be a consideration then.
Edited by Lady of McCamley - 1/28/16 at 11:12pm