Reference: http://www.alfawzan.af.org.sa/node/15413
Question: Is it permissible for a young child to lead the prayer?
Response: Yes, if he is able to distinguish [between right and wrong], and is the best of the people (congregation) at reciting [the Qur.aan] – then it is permissible. [This is] because during the time of the Prophet ﷺ a group of companions were in the desert, and amongst them was a young child who was conscientious – having memorised the Qur.aan. And he had attained a good level at reciting the Qur.aan [too], so they ushered him forward to lead them in prayer – and this [particular incident had taken place] during the time of the Messenger ﷺ and he did not rebuke them for doing that.