If the 10 year old is a female, who has reached her shar'i age of bulugh, then yes, she will need to pay the kaffarah of 'feeding 60 poor', along with doing the qadha' of that day.
In these matters it is crucial to refer back to your Marja' taqleed, for the specific ruling, but from the view of A. U. Seyid Sistani, if you were confident you did not have to redo those days as qadha', you do not need to pay kaffarah, but you do need to redo those days as qadha`.
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