So ideally finding a death record for William Malcolm and Seeing if their’s exisiting records that can go back even further on what we’ve already found.
I already posted a link to William's death notice-
Downpatrick Recorder. 5 Apr.1867: Malcolm- March 31. at his residence, Saul-street, Downpatrick, Constable William Malcolm, aged sixty-one years.
Registration of deaths started in 1864 but the very early one are not yet viewable on Irish Genealogy. You can view if on GRONI's website after registering (free) and buying a few credits-
https://geni.nidirect.gov.uk/However, you may not get much more detail than what's in the newspaper note (except, of course, cause of death should be listed).
I looked for Isabella (Malcolm) Barber's family in Derry City Cemetery records online which list place of birth, names of parents, etc. but none of that family seem to be there.