You'll need to start in Canada and check all possible records there before looking in Ireland.
Submitted family tree has some sources you can start looking at (there is more on Family search, just search for 'simon mcveety' in 'canada.'
https://www.familysearch.org/ark:/61903/2:2:3FWX-YVLEarly passenger records are not complete and it's really a hit or miss matter if you can find something but if anything does survive for c1820 it might just list name, ages & occupations although could just list adults & number of children.
Since birth registration in Ireland didn't start until 1864 you need to see if church records survive (not all that do survive are online). A church marriage record would probably just list date, bride & groom, whilst a baptism might just have date of baptism, child's name & parents (or maybe just father). A townland may not be listed in church records.
If they were Church of Ireland the church registers may not exist any longer- many pre-1870 COI registers were sent to Dublin for safekeeping which is ironic because most there were destroyed in fire at Four Courts during Civil War (1922).
This page says James McVeety born Anna in County Cavan.
If that is correct them the civil parish of Annagh is one possibility-
https://www.townlands.ie/cavan/annagh/This map shows the
current churches in Cavan but there might be others that closed.
https://www.ireland.anglican.org/find-a-church/parish/13700/annagh-belturbetMore on Annagh Civil Parish and what records might be available-
https://www.familysearch.org/wiki/en/Annagh_Civil_Parish,_County_Cavan,_Ireland_Genealogyhttps://www.genuki.org.uk/big/irl/CAV/AnnaNaturally you should check resources in Canada such as gravestones, local histories, census & vital records, etc. as well as seeing if other descendants have more details.