The Collaborative International Dictionary of English v.0.48:

Nanny \Nan"ny\, n.
   1. A diminutive of Ann or Anne, the proper name.
      [1913 Webster]

   Nanny goat, a female goat. [Colloq.]
      [1913 Webster] Nanny

The Collaborative International Dictionary of English v.0.48:

Nanny \Nan"ny\, Nannie \Nan"nie\(n[a^]n"n[y^]), n.; pl.
   nannies.
   1. a caretaker for a child; a child's nurse; a nursemaid.
      [PJC]

   2. Grandmother; -- a child's word, used especially as a form
      of address. See also nana.
      [PJC]

WordNet (r) 3.0 (2006):

nanny
    n 1: a woman who is the custodian of children [syn: nanny,
         nursemaid, nurse]
    2: female goat [syn: nanny, nanny-goat, she-goat]

Moby Thesaurus II by Grady Ward, 1.0:

45 Moby Thesaurus words for "nanny":
   Partlet, amah, ayah, biddy, billy, billy goat, bitch, bossy,
   brood mare, buck, cow, doe, doeling, dry nurse, ewe, ewe lamb,
   filly, goat, guinea hen, gyp, he-goat, heifer, hen, hind, jenny,
   kid, lioness, mammy, mare, mountain goat, nanny goat, nurse,
   nursemaid, nurserymaid, peahen, roe, she-bear, she-goat, she-lion,
   sitter, slut, sow, tigress, vixen, wet nurse