The key here is that you write she is "lanky and a string bean like her dad." She is reflecting her genetics. The fact the doctor is fine with her development is great. So is the fact you are an attentive mom who is keeping tabs on the eating issue, with the doctor's help--rather than going nuts and going online to self-diagnose her with a thousand problems without a doctor's input.
Our godson was very tiny--short and thin. As a baby and toddler, some doctors started worrying his parents about it, sending them to specialists and eating studies and throwing around terrifying terms like "failure to thrive" - all based on his size and NOT on whether he was getting enough nutrients (he was) or anything else. One day a new doctor actually looked at the mom and dad. Dad is short and very skinny. Mom is very short though heavier. This doctor finally said: "It's genetic. You're small people and your son is small. He's fine."
All that heartache and all those pokes and prods when if some doctor had just taken one good look at the mom and dad earlier, things would have made sense!
Do keep watch on her eating, and if she doesn't grow at whatever pace is good for her, yes, get her checked and ensure she's absorbing nutrients (which can be an issue in some conditions).
But when people, especially random strangers you've just encountered on the playground etc., say "She looks so tiny for her age" or, heaven forbid, anything more critical, tell them: "She's built like her dad and he's thin." If they persist: "Her doctor says she's fine. Are you a pediatrician, yourself?" That should silence 'em.