I searched the Irish Family History Foundation's database. Geneological rcds for Co. Louth are in it. There are over 1,000 B/M rcds for the surname White there.
I found B rcds for three of the named children abt the dates you listed in the parish of Cooley. The only one not B in Cooley is Jane. Also, Michael is spelled "Michal."
For John White B 1820 +/- 4 yrs, I found 9 B rcds, nearly 1 each yr. One of these MAY be for your ancestor. However, only abt 1/2 of the Louth parishes were keeping rcds at this time. Your chances are abt 50:50.
For Catharine Rowe B 1825 +/- 4yrs, I found 0 B rcds. The event wasn't rcd'd, or rcd has been lost.
For a marriage for the names John and Catharine in 1833 +/- 4yrs, I could find marriages for each name, but not in the same yr and parish. This is NO MATCH. They may have married elsewhere, or the event was either not rcd'd or rcd was lost.
Google the Foundation's name to lead you to the database. Post a msg on Genforum to tell me of your search results.