Praise be to Allah.
If the dirt that has gotten onto the Mushaf is removed, and there is no offensive odour left, then there is nothing wrong with reading and memorizing from it.
But if there is a smell or there is some trace of dirt left on it that cannot be removed, there is nothing wrong with burning it and bringing another one, out of respect for the Book of Allaah and the wish not to leave any impurity or bad smell on it.
May Allaah reward you with good for your respect towards the Book of your Lord and your asking such a question which is indicative – in sha Allaah – of goodness and religious commitment. We ask Allaah to make it easy for your daughter to memorize the Qur’aan and act according to it.
And Allaah knows best.