She is thirteen years old and she does not fast Ramadaan
Question

A 12 or 13 years old girl does not fast during Ramadaan, should she or her family expiate? Should she fast? What should she do if she does not fast?.
Praise be to Allah.A woman becomes accountable when she fulfils the conditions, namely being Muslim, being of sound mind and being an adult. Adulthood is reached when she menstruates, emits maniy with desire or has a wet dream; or by the growth of hair around the private part; or when she reaches the age of fifteen. If this girls meets any of the conditions of being accountable, then fasting is obligatory for her, and she has to make up the fasts that she did not observe at the time when she was accountable. If she did not meet the conditions then she was not accountable and she does not have to do anything. 
And Allaah is the source of strength. May Allaah send blessings and peace upon our Prophet Muhammad and his family and companions. End quote. 
Standing Committee for Academic Research and Issuing Fatwas (10/146، 147) .