What is the ruling on a young girl praying without a head covering?

If a girl has not reached puberty, her prayers are valid, based on the Prophet's (peace be upon him) saying: "Allah does not accept the prayer of a menstruating woman except with a head covering (khimar)." This indicates that a non-menstruating woman (which includes a pre-pubescent girl) has no fault in praying without a head covering. However, her praying with a head covering is better and more complete if she is seven years old or older. As for those younger than seven, male or female, they are not obligated to pray, based on the Prophet's (peace be upon him) saying: "Command your children to pray when they are seven, and beat them for it when they are ten, and separate them in their beds."