Dear Skelly,
Your daughter's weight in and of itself doesn't indicate she is anorexic. She is actually approximately at the 20% for children her age, so her weight is not dramatically low. In any weight distribution there are going to be children at the low end of the spectrum, some at the high end of the spectrum, with most children falling somewhere in the broad middle range.
Anorexia is characterized by an intense fear of gaining weight or becoming fat, an intense drive for thinness, along with severe food restriction in order to lose weight. People who display anorexia (and approx. 95% of anorexics are female) display a distorted view of their bodies, often regarding themselves as overweight when, in fact, they are not. Anorexics often deny that they have a problem.
Based on these criteria, it is probable that your daughter does not meet the requirements for a diagnosis of anorexia, but she may be at risk for eating disorder and it is worthwhile to keep this in mind. It will be important to refrain from engaging in struggles with her around eating, weight, etc. Your approach in having her pediatrician guide her toward some weight gain on a gradual basis is sound. Just be careful not to over-invest in her weight or eating habits.
If you choose to have her evaluated by a mental health professional, be sure it is someone who is a specialist in eating disorders. This is a sub-specialty of mental health practice.
My brother with through a long process with his daughter when she battled anorexia. If you would like to talk further, please e-mail me at ***@****.