Moore was raised in County Cork in an Irish-speaking household. His father, Peadar Ó hAnnracháin (born 1873) (also known as Peter/Peadar Hourihane and Peadar O'Hourihane) was a writer and poet, and a staunch supporter of the Irish language. Peadar, a son of Seaghan Ó hAnnracháin (born 1834) and Máire Ní Dhonabháin (also born 1834) and who was one of the first organisers for Conradh na Gaeilge (Gaelic League), was twice imprisoned by the British during the Irish Civil War. Peadar lived with his parents and his sister, Áine Ní Annracháin (born 1885), and his niece, Máirín Ní Dhiomasaig (born 1903), at 14 Poundlick, Skibbereen, County Cork in 1911. He also wrote for the "Southern Star" newspaper for many years and had been its editor.