This is a question that has come up multiple times over the years, but Demi Moore never appeared on Little House on the Prairie.
She did begin acting around the time the show was airing (her first credit appears in 1981 in Choices, before getting her break in General Hospital in the following year), so there is a possibility she played one of the non-speaking roles in the show at some point (such as a young Sean Penn did), but this has never been confirmed by the actress or anyone else.
