This is an interesting topic that took an odd turn. Age of accountability can be a sticky conversation in some complex situations, but generally considered 8 years old. However, as far as children sinning:
"They cannot sin, for power is not given unto Satan to tempt little children, until they begin to become accountable before me" (see D&C 29:46–47).
Which lends itself to the sidebar conversation around all bad things/ actions being attributed to Satan. We all agree that little kids do "bad" things - but if Satan can't tempt them, what caused them?