The Miss Nanny robot is a utility robot with female programming. They were primarily created by General Atomics International for use in the household, which is why they look very similar to their "male"-counterpart the Mister Handy models.
The Miss Nanny design was geared mainly towards caretaking tasks, intended for parents of children of all ages. Its specialized programming included disciplinary and behavioral management skills (with an optional corporal punishment mode that had to be manually turned on by parents), vocal tonality analysis routines allowing it to interpret the needs of its charges (even infants) and hazard detection matrices for childproofing rooms.
Miss Nanny units seem to typically speak with a French accent and have a white plating. This may have been done to make them better fit the French maid stereotype, which in turn would explain the Mister Handy's English accent to fit the English butler stereotype, and the Mister Gutsies voice would play to the American soldier stereotype. Pearl in the Far Harbor add-on speaks with a vague English accent, proving that Miss Nanny models have more than just one voice module.
Miss Nanny and Mister Gutsy units are both sometimes considered as being variations of the Mister Handy model by consumers as well as by their creators. This is logical because they were created by the very same company who specializes in these type of robots.
It appears that there is no standard "Miss Nanny" NPC around, or at least not anymore, unlike the Mister Handy and Mister Gutsy NPCs.