Praise be to Allah.
This is a wonderful thing for such a young person (11 years old) living in a non-Muslim country and deviant society to accomplish. The fact that she has not given her name is a sign of sincerity, in sha Allaah. I think that this should only be announced for the purposes of encouraging others to do the same. The affair should be limited to a small gathering where some relatives or friends invite a few of the girl’s friends, tell them of her achievement in completing the Qur’aan in order to encourage them - not to show off or boast - and some of the mothers say a few words about the greatness of the Qur’aan, the importance of reading it and how the Muslim should treat the Qur’aan. Or this girl could invite her friends to a meal to mark the occasion and give thanks for this blessing. There is nothing wrong with such activities, as long as one is careful not to let it turn into a celebration.
It is clear from the above that celebrating a person’s completion of reciting or memorizing the Qur’aan, inviting people and offering food, is an action in which there is a risk of two fitnahs (temptations):
(1) that it might be an occasion for showing off and boasting, and
(2) that it may constitute bid’ah, if people believe that such celebrations are part of the religion and must be held every time a person completes the reading of the Qur’aan. The first danger may be avoided by striving within oneself to be sincere towards Allaah, and the second by restricting the invitees to a small number of family and friends.
We should not hold such gatherings regularly, lest people think it is a part of the Sunnah I ask Allaah to increase His blessings upon you and to give you the strength to memorize Qur’aan and Sincerity in speech and deeds.