Unfortantely baptism records going back as far as the 1700s are rare in Ireland. So the chances of finding one for Dominic are small.
There are a few websites that hold records.Hopefuly you may be able to find something.
www.rootsireland.ie has a searchable database of Catholic Church records. There is a fee for using the site but it can be purchased on a daily, monthly or yearly basis.
Civil records are available on the link below
The census 1901/1911 census are available to search on http://www.census.nationalarchives.ie/
Records of a place can provide useful information about where your ancestors lived. The main sources for records of place are Griffith's Valuation, the Tithe Applotment Books, estate papers and maps.They are available at https://www.nli.ie/en/griffiths-valuation.aspx