The word ᴹQ. yat (yak-) “goat” appeared in the Declension of Nouns from the early 1930s (PE21/24).
Conceptual Development: In the Qenya Lexicon of the 1910s and Early Qenya Word-lists of the 1920s, ᴱQ. yakko was “ox” (QL/105; PE16/132). In Common Eldarin: Noun Structure of the early 1950s, Tolkien gave the possibly-related primitive form ✶najak- for “goat”, with masculine and feminine variants ✶najakō “he-goat” and ✶naikē “she-goat” (PE21/82).
Neo-Quenya: Helge Fauskanger used ᴺQ. naico for (male?) “goat” in his NQNT (NQNT) as a derivative of ✶najakō, and I would recommend this over ᴹQ. yat for this purpose. However, I’d recommend ᴺQ. nyéni for a female goat (adapted from ᴱQ. nyéni) since it (a) is more distinctive than ✱naice and (b) does not conflict with ᴹQ. naike “sharp pain”; Helge Fauskanger used nyéni in NQNT as well.