Since children were not frequently mentioned, what is known about them comes from the description of adults and objects found in the tombs of children.
Children often took part in activities one would consider for adults only. They would at time fulfill economic and social tasks which resulted in them being portrayed as diminutive adults. The older they got the more demanding theses roles got. Their economic role was that of a helpmate.
There is not much documents on how girls were treated as literary sources concentrated more on how fathers instructed their sons. Mothers taught the daughters and father taught the sons.
Children were cherished for the role they played for preserving the legacy of their parents and carrying on the bloodline.
Sons and daughters (to a lesser extent) inherited the possessions, social standing, profession and offices of their parents.
There was little contact between children of different classes and children of higher class were less likely to suffer from malnutrition. As orphaned children were common to find, they grew up in villages with their extended family.
Credit for information: http://www.reshafim.org.il/ad/egypt/people/childhood.htm