All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
It is permissible for the woman or the female child to have her ears pierced to wear ornament. During his lifetime, the Prophet (PBUH) approved that women wear gold earrings, as indicated in the following Hadith: Jabir b. 'Abdullah reported:
I observed prayer with the Messenger of Allah (PBUH) on the 'Id day. He commenced with prayer before the sermon without Adhan and Iqama. He then stood up leaning on Bilal, and he commanded (them) to be on guard (against evil for the sake of) Allah, and he exhorted (them) on obedience to Him, and he preached to the people and admonished them. He then walked on till he came to the women and preached to them and admonished them, and asked them to give alms, for most of them are the fuel for Hell. A woman having a dark spot on the cheek stood up and said: Why is it so, Messenger of Allah? He said: For you grumble often and show ingratitude to your spouse. And then they began to give alms out of their ornaments such as their earrings and rings which they threw on to the cloth of Bilal. {Related in Sahih Muslim}.
Ibn Hajar al-Haitami (May Allah have mercy on him)said: "It is absolutely forbidden to pierce the ears of the male child, whilst it is permissible for the female child because is a customary practice-in the past and present-intended for ornament purposes, and was deemed permissible by the Prophet (PBUH)………." {Tohfat al-Mohtaj, V.9:196}. And Allah the Almighty knows best.