The UN needs to keep it as simple as possible for a global audience. They also need to remove all connotations that have become associated with other uses of the word girl, and to clarify the intended meaning.
Many uses of the word "girl" have lost the implications of youth that they once carried. "Daughter" means progeny, and implies a relationship between parent and child, but they want to include concern for children without parents. And "female" is not on the list of 850 Basic English words. (Neither is "international", but as that's the basic charter of the UN, they have no real alternative.)
If it helps, don't think of "girl child" as a phrase, simply consider "child" as a qualifier of "girl".