Thank you both so much. I was very excited to get answers.
'Hallmark', thanks to you, now I have a birth date for Margaret, a specific dwelling place, as well as birth years for her two children born in Ireland and her mother's burial in a Presbyterian church.
Margaret had five sons in Jamberoo, NSW. The eldest was also called John, which I find a bit weird. The family became very successful dairy farmers; and sons and grandsons also successful in professions such as teaching (Senior Inspector of Schools), law & medicine.
I found a Civil Marriage Certificate extract for Margaret SEYMOUR and James WALKER, in Parish/District of Dungannon, Co Tyrone. The address for both is given as Aughnacloy. [James was born in Aughnacloy to John WALKER and Isabelle (Bell) IRVINE according to his Death Certificate.] Both fathers are recorded as being farmers. At the bottom of the certificate is typed: "Aughnacloy or Carnteel Parish C.O.I." I'm not sure why this is different from the top where it states "Dungannon". I also don't know what C.O.I. means.
The ship's records state for both of them that parents were "both dead". This explains not finding Harper in later indexes; however there may be relatives such as surviving uncles and brothers. There are some more SEYMOUR listings under Co Monaghan. 'Hallmark' has indicated a link between the two counties for this family.
Also, the ship's records stated Margaret's Native Place and County as "Omagh - Co.Monaghan", which is why I thought she was born in Omagh. Her death certificate only mentions county. I suppose she may have been born in one place and moved somewhere else she identified as 'native place'. It just goes to show you can't always trust the records and must cross reference and think laterally.
There is a John and a James WALKER in Co Tyrone on the Flax Growers Index in late 1700s. I suspect, but will not assume, they are related to Margaret's James.
I was interested in Jane's burial in a Presbyterian church. I have been assuming C. of Ireland/England. Oh yes, assumptions again. lol.
Once again thank you both for your help
It is a fascinating meander back in time.
Cheers,
Julie