Where do the names Thomas and Anne Hart come from?
I think you need to do some more research to obtain some more facts
..
John Egan who died 1916 at Hillgrove - his death cert records his mother as Margaret
There is a catholic baptism for a John Egan on 15 Nov 1839 at Roscommon, Ireland
Father John (Johannis) Egan and mother Rosae Farrell.
You need to verify it is for your John, as the name is very common.
I would suggest you find Johns immigration record, and his marriage, to know if you are on the right track.
NSW birth records for his children can often give important information about parents.