Mathew Dunn is listed in Lathbirget in the 1828 tithes:
There’s a possible death for Peter Dunn aged 46 registered in Newry on 14.4.1871. Your Peter & Ann don’t seem to have had any children born after 1871 which would tie in. You can view the original certificate on-line on the GRONI website, using the “search registrations” option:
You will need to open an account and buy some credits. It costs £2.50 (sterling) to a view a certificate.
I presume this is his widow in 1901, so we know he died somewhere between 1870 and 1901. The 1871 death is the only adult Peter Dunn(e) death in the area in that timespan.
There are very few other early records that are likely to list this family. You may struggle to find much more about their lives in the early 1800s.
Griffiths Valuation for 1864 lists Peter Dunne farming on plot 23(j) in Latbirget with a Patrick Dunne farming beside him on 23 (i). That would suggest they were related. This looks to be Patrick’s death in 1878 aged 70:
So who was he? An uncle perhaps?
Mary Dunn, widow of Michael here:
Ann Dunn, farmer’s widow here:
The Valuation revision records for Latbirget (on the PRONI website) show both plots 23(i) & 23 (j) changing to Ann Dunn in 1881. That may indicate their husbands’ had just died but the Griffiths clerks dates were often out by a few years so it’s just indicative.