My son never had an appetite at all until 7. I spent years ensuring that he drank enough milk, told stories about 'this piece of potato really wants to be with its brother potato, wait for me brother, please eat me....' as I fed him almost every meal. I once tried leaving him to get hungry, he remained happy for 2 days and ate nothing.
All this suddenly changed when I gave him fish oils to help his dyslexia, his reading didn't really improve but after 3 days he started to eat - he went from being the shortest in the class to tallest in one year.
Many children with dyslexia or development delay have immature nervous systems, my son just wasn't receiving hunger signals. There was nothing emotional about it at all.
Your daughter is still very young, if you see a psychologist make sure eating and food doesn't become a bigger worry to her.
I would ensure that she gets enough milk, that what she does eat is full of vitamins and protein, tell her stories about the food to get it down her, have the patience of a saint, and I'm sure this will all right itself with time.
Its worrying, hard work and frustrating, I did it for 7 years, but sometimes we just have to wait for children to mature.
Helen