Is it farther or further?
"children's nurse," 1795, from widespread child's word for "female adult other than mother" (cf. Greek nanna "aunt"). The word also is a nickname form of the fem. proper name Ann, which probably is the sense in nanny goat (1788, cf. billy goat). Nanny-house "brothel" is slang from c.1700. Nanny state, in reference to overintrusive government policies is attested by 1987, the term associated with British political leader Margaret Thatcher, who criticized the tendency.
"to be unduly protective," 1954, from nanny (n.). Related: Nannied; nannying.