If you were unhappy with your doctors diagnosis, I would suggest that you get another. Were you in the room with your daughter when they discussed her weightloss? I would be concerned that your daughter weighs that little, eats healthily and over exercises. These are very typical symptoms of an eating disorder.
I would go back to another doctor find their opinion and take it from there, you will also be able to ask them their opinion on how she can put on weight.
Her BMI is around 14.5 this is severely underweight. Therefore it is very important that she does put on weight. These are some of the consquences of being underweight;
Hormones regulating menstruation and fertility are disrupted, immunity is compromised and infections develop, and nutritional deficiencies may produce hair loss, anemia, and osteoporosis (bone thinning). In addition, emotional changes are inevitable, including social withdrawal, irritability, depression, and sleep disorders.
I really hope that your daughter gets whatever help she may need soon!