I reckon Dennis Dempsey (born in 1795 according to the death record) was probably baptised at St Peters in Drogheda, Ireland on 14 March 1795 to parents John Dempsey and Mary Brogan. Siblings are Bernard 3 May 1788, Patt 10 Jul 1789 and Nicholas 21 Aug 1790. Some of the godparents were Rose Brogan and Dennis Dempsey... perhaps they were siblings of the parents.
There are some indications that they may have come from West Meath... but nothing more yet.