S01E07: The Babysitters

Roped into babysitting little Egbert, the child of a friend, Fred and Barney take the tot over to the pal Joe Rockhead's house to watch the fights on television. Egbert befriends Joe's pet runtosaurus and dresses the creature up in his baby clothes, which results in chaos when the pet--whom Fred and Barney mistake for the baby--escapes from the house and dashes up a tree.