Scott, there are many, many hemoglobinopathies that reduce H&H results (Hemoglobin/Hematocrit). As a lab tech I have run into numerous oddities in my near 18 ears of experience. While I am not a doctor and not have seen the results of your child's CBC it would be extremely presumptive to guess at what could be going on... that is why the physician caring for your child is being cautious in throwing out a diagnosis. Have they run any Cold Agglutinin or Allo/Auto Antibody profiles yet? And, is your daughter old enough to mensus? Not trying to be nosing, just trying to get a better picture of what is going on. Trust the professionals, they are doing everything they can. We lab techs take our job very seriously especially when we hear that there is a sick child at the other end of the tests we are running.
Keep faith that our prayers are working and that all will be okay in the end no matter the diagnosis.