I do research the Domingue family of LA but I do not know of your father specifically. I would suggest that you get a copy of your father's death certificate. It's possible that his parents' names are listed there. If not, next I would look for a birth certificate which will give his mother's name and usually the father's name too. Another source would be church records, for a baptism. I hope this helps. If you do find his parents' names and still need some help going back further, let me know and I'll see what I can do to help you.