Rocker, the name of the Bonanza episode you speak of is THE MANY FACES OF GIDEON FLINCH. The girl is Sue Ane Langdon, who was also the one spanked in Gunsmoke. She is more of a redhead in the Bonanaza episode.
Little Joe accuses her of stealing his wallet so he puts her over his shoulder and marches her to the sherriff. He gives her 3 swats for her protesting.