I searched the Irish Family History Foundation's database for Co. Louth. Rcds B4 1840 are sparse.
1. For Matthew Hart, B abt 1844, there is 1 B rcd in 1837. This is the only rcd'd Matthew with this surname in Louth between 1700 and 1921. A view of the detailed rcd SHOULD show the parents' names. This info can validate/invalidate the rcd. Because this date differs so much from yours, there is only a small chance this is for your ancestor.
2. For Peter Hart, there are no B rcds prior to 1842 and 1 M rcd in 1841, Drogheda parish. For Ann(e) King, there are 4 M rcds, but none in 1841, and none in Drogheda. Either rcds of this event didn't survive or they married elsewhere.
3. For Ann(e) King, B abt 1822, there are 6 B rcds: 1820, 1820, 1823, 1824, 1825, & 1826. One of these may be your ancestor.
Google the Foundation's name to lead you to the database. Post a reply to Genforum to tell me your results.