Ah, I was wondering about that. I have never heard the word before today. It's sort of funny to contrast the words that are thought early on here on Duolingo versus what we learnt in school. I can still remember my little sister coming home from her first day at school some twenty odd years ago and pointing saying "sin doras. sin fuinneog".
Sé troigh sé a bhí an damhán alla Nuair a dhéanadh screá dó anuas faoin talamh Bhuail sé a chos in aghaidh an bhalla Agus bhris sé a dhroim Ceard a rinne sé Bhris sé a dhroim Ó bhris sé a dhroim Bhris sé a dhroim That's what he did
Ba dheabhall an mac é an damhán alla Nuair a dhéanadh screá dó anuas faoin talamh Thosaigh sé ag glaoch ar a mháma Mar do bhí sé tinn Cén chaoi a raibh sé ? Bhí sé tinn Ó bhí sé tinn Bhí sé tinn Cén fáth nach mbeadh
McBain's An Etymological Dictionary of the Gaelic Language (http://www.ceantar.org/Dicts/MB2/) is wonderful on these questions. It's a Scottish Gaelic dictionary, but often gives the related Irish words. The term in that language is "damhan-allaidh" by the way, and for the etymology of damh: ox, stag, so Irish, Old Irish dam, Cornish da, dama, Middle Breton dauat, sheep, Breton danvad, sheep, demm, roe, *damo-s; Latin dâma, damma, deer; Greek @Gdamálcs, a stier, @Gdámalis, a calf; Sanskrit damya, untamed stier. Allied is English tame, Latin domare, English domestic, etc.
I feel like the pronunciation of "damhán" here is slightly different from the one in the sentence "An luch agus an damhán alla." (https://www.duolingo.com/comment/4290839). Here it sound more like "dau" and in the other one it sounds more like "dwa" (in the sentence with the cat even more so). Unfortunately Focloir doesn't have any pronunciation for it and Forvo gives more of an "dua" sound (but there is only one example, so it's not very conclusive).
So which one should I try to use?
(Gonna post this under the other sentence too.)