There are some scholars who consider women's voice as awrah to be hidden and concealed; they are of the view that her voice may arouse lustful thoughts in men. However, this view has been rejected by the majority of scholars. It is simply unacceptable based on evidence of scripture and reason. The Qur'a and the Sunnah are replete with examples of women speaking to men and vice versa. The mothers of the faithful used to teach and lecture to men and women as is well known from the precedents of Aishah as well as others.
Furthermore, we learn from the authentic traditions that Prophet (peace be upon him) allowed girls to sing on a number of occasions, and he objected to those who condemned and disapproved of it on the Eid day. He attended a wedding reception where he heard the singing. As they saw him, they added the phrase, 'among us is a prophet who knows what happens tomorrow', upon hearing it, he told them, to cut out the phrase and continue singing as they were.
If girls are allowed to sing in a mixed gathering, then there is no reason to forbid them from reading the Qur'an, which is indeed an act of worship.
Having said this, it is important to point out that both women and women are required to observe the Islamic etiquettes and adhere to acceptable standards of interaction (between males and females) on all occasions, including avoiding expressions and mannerisms that arouse carnal desires and emotions.