Nannies, sometimes called babysitters or nurse maids, were individuals who took care of children and babies, similar to governesses.
When Donna Noble called Matron Cofelia of the Five-Straighten Classabindi Nursery Fleet an "outer space super-nanny," she seemed content with the title. (TV: Partners in Crime)
Clara Oswald, a companion of the Eleventh Doctor, became a nanny to Angie and Artie Maitland after their mother died. Her job included watching over them when their father, George Maitland, wasn't at home, and teaching them. She made Artie read the book Summer Falls. Whilst Clara was sleeping, the Doctor once took over her nanny duties. (TV: The Bells of Saint John, The Name of the Doctor) Once George was coping well enough on his own, Clara gave up the position (PROSE: Normality) and moved on to a teaching job at Coal Hill School. (TV: The Day of the Doctor)
Mamlaurea was Susan's nanny for most of her time on Gallifrey. (PROSE: Lungbarrow) Susan, on her part, babysat six-year-old Malcolm every Saturday during her stay in 1963 London until his aunt Junie arrived on 4 April. (PROSE: Time and Relative)
Mrs Mantovani was Kazran Sardick's babysitter until age twelve, then the Eleventh Doctor arranged for her to win the lottery and took her place for Christmas. (TV: A Christmas Carol)
After Jackson Lake was, thanks to the Tenth Doctor, reunited with his son Frederic on 25 December 1851, he appointed Rosita as Frederick's "nurse maid". (TV: The Next Doctor)
The Twelfth Doctor was relieved that Ross and Gretchen Carlisle were in fact people who would shoot the Doctor dead if he turned out to be a Dalek spy and not "armed babysitters" as he originally thought, because he claimed to hate babysitters. (TV: Into the Dalek)
The Seventh Doctor compared the Panjistri to the Kirithons' nannies. (PROSE: Timewyrm: Apocalypse)