Ireland the place I am from = Éire - an áit as dom
However it doesnt flow very well that way in Irish because thats not the usual way of saying it.
Because it would usually be said like "Is as Éirinn dom" if you wanted to say "Im from Ireland"
or most of the time we just say "Is mise Éireannach" (im Irish) so to see it any other way looks very strange.
Because it looks strange when people read "an áit as dom" they might not get it right away.
lancing at it it reads as "the place from for me"
You'd have to look for awhile and remember that "Cad as duit?" means "where are you from" and then realise that it means "the place I am from"
Its a bit obscure to be honest.
You would probably be best going with "Éire - mo bhaile"
Although that also read as Ireland - my town
I cant really come up with any good alternatives.
Maybe,
Éire - an áit a rugadh mé = Ireland - the place I was born
Is i Eire mo ait dhuchais makes no sense.
You could say,
Éire - mo áit dúchais = Ireland - my native place
OR
Éire - mo thír dhúchais = Ireland - my homeland (native land)