With an EE rooster over BR hen, you'd get sexlinks, basically. The males will have barring, the females will be mostly black or black with brown/gold on the chest areas. Mine were BR roo over Ameraucana hen, so they all got some barring.
That bird is not a standard color for an Ameraucana. Cannot see her legs, but her color is not one of the 8 accepted colors. If she didn't come from a breeder, she isn't an Ameraucana. None of the big hatcheries sell Ameraucanas or Araucanas. This site may help. These are the breeders of several of my BBS Ameraucanas: http://creefarm.fateback.com/ameraucana.html