T.W.
Aack! This is the most frustrating thing when it comes to having children in my opinion. All three of my children barely eat. I wonder how they sustain life honestly. They just run run run!!! That being said, after having stressed forever with my first, my doctor finally told me that he is perfectly healthy, growing right on schedule and to remember that children have a way of eating exactly what they need as far as quantity. As adults we don't really have a shut off and typically our need to eat is based on love of eating therefore we eat too much.
If it will make you feel better, track exactly what she eats and check the calories. You will probably find that she is eating just the right amount of calories for her size. I wouldn't hold back on what she drinks, milk and juice all have calories as well and can make up where she might be lacking in food calories. Try things like vegetable juice as well. If all she will take in is beverages, maybe you just go with it ya know.
One thing I can assure you is, these eating habits are phases and all three of mine go a few months at a time barely eating then they eat like a horse. You can go have her measured at the docs. I am sure she is fine.