I searched baptisms/births on www.rootsireland.ie/ for the children of Edward and Mary Gough years 1838 + - 10 years in Waterford and got 3 results: Thomas 1830 Michael 1840 & Patrick 1842.
It is possible to check the parish and it was Stradbally RC for all 3.
When I extended the search to + - 20 years I got 3 more: John 1849 Edward 1851 & another Thomas 1856
There is also a record of the marriage of Edward & Mary in 1828 in Waterford. If you purchase this it will give you Mary's last name and you or I could then search for the children to see which belong to them.