From your height measurements, she is just below the 75th percentile. You did not write her weight, so I cannot evaluate if she is underweight or normal. If her Doctor is stating her weight is fine, then she is normally thin. For her age, she needs to consume approximately 1200+ calories per day. If she is, as you stated she is not a fussy eater, then she growing normally. Some people are naturally thin. It maybe genetic if there are thin females in your family. When she goes into adolescent, she may gain weight as she develops. Thank you for your question.
If her doctor says she is in good health, why do you worry? Some people are naturally thin, yet healthy. I come from such a family. There were always notes home from the school telling my parents that we were underweight. They really hassled them about one brother who was an ectomorph to beat all ectomorphs. When he joined the navy with he was 17 he was 5'10" and weighed 116 lbs. Well my siblings and I are now in our late 70's to late 80's, still slender and in good health for our ages.