I can fill in a few gaps for you. The Thomas Robb died 1886 is your ancestor so I'll start with him.
Thomas Robb (c1825-19 Jan.1886 Melbourne, Vic.), painter, m.(1853 Saintfield COI) Anna Cunningham; m.(1858 Magheragall) Mary Ferguson McNeight/McNight (c1837-11 Feb.1911 Belfast)
? 1852 Belfast Directory- Lisburn: Robb, Mr., painter, Railway Street
https://www.irishgenealogy.ie/files/civil/marriage_returns/marriages_1853/09452/5424923.pdf (father Andrew, soldier)
https://www.irishgenealogy.ie/files/civil/marriage_returns/marriages_1858/09553/5463392.pdf (Castle St. Lisburn, father Andrew, soldier)
1861 Belfast Directory- Lisburn: Robb, Thomas, painter, Castle Street. (same address as 1858 marriage)
The Age [Melbourne], 19 June 1886: Casualties And Offences. The following persons were taken yesterday to the Melbourne Hospital:- Thomas Robb, aged 60, painter, residing Westwood-place, off Bourke-street east; he was found insensible at corner of Russell and Bourke streets shortly after eleven o’clock Sunday night, and died in hospital at five a.m. yesterday...
Witness [Belfast], 2 Apr.1886: ROBB- January 19, at Melbourne, Australia, of apoplexy, Mr. Thomas Robb, formerly of Lisburn. (this is a standard format for the period but obviously by that date his family in Ireland must have gotten news of his death)
https://www.irishgenealogy.ie/files/civil/deaths_returns/deaths_1911/05406/4510275.pdf (widow of Thomas Robb a painter, informant son-in-law Thomas Moore)
Belfast Newsletter, 13 Feb.1911: ROBB- February 11, at 27, Hughenden Avenue, Belfast, Mary F. Robb, widow of the late Thomas Robb, formerly of Lisburn. Funeral private.
Children:
1. Jane Anna Robb (c1859 Co.Antrim) m. Thomas Moore.
2. John Robb (1861 Ireland).
3. Elizabeth Robb (1864 Australia).
Jane Anna Robb (c1859 Co.Antrim-aft.1941) m.(1882 Dublin) Thomas Moore (d.25 Dec. 1940), commercial traveller
https://www.irishgenealogy.ie/files/civil/marriage_returns/marriages_1882/10976/8012320.pdf (witness- Lizzie Robb)
Belfast Newsletter, 5 Sept.1882: MOORE-ROBB-September _, at Adelaide Road Presbyterian Church, Dublin, by the Rev. Robert M'_ Edgar, M.A., Thomas Moore, youngest son of Andrew Moore, Belfast, to Jane Anna (Jennie), eldest daughter of Thomas Robb, late of Lisburn.
https://www.census.nationalarchives.ie/pages/1901/Down/Bangor/Princetown_Road/1253176/https://www.census.nationalarchives.ie/pages/1911/Antrim/Clifton__Belfast_Urban_No__2/Hughenden_Avenue/134432/ (5 ch./2 liv.)
Moore Thomas of 159 Stranmillis Road Belfast retired commercial traveller died 25 December 1940 Probate Belfast 21 March [1941] to Jane Anna Moore the widow. Effects £63 15s. 11d.
I've found 4 of the 5 children-
1.
John Robb Moore (1885 Belfast-aft.1901)
https://www.irishgenealogy.ie/files/civil/birth_returns/births_1885/02650/1977111.pdf 2.
Thomas Andrew Moore (1887 Belfast)
https://www.irishgenealogy.ie/files/civil/birth_returns/births_1887/02574/1951603.pdf 3.
Reginald Heber McNeight Moore (1890 Belfast)
https://www.irishgenealogy.ie/files/civil/cert_amends/cert_1890/1899000a.pdf 4.
Cecil Graham Moore (1889 Belfast-aft.1911)
https://www.irishgenealogy.ie/files/civil/birth_returns/births_1889/02477/1919547.pdf Elizabeth "Lizzie" Robb (c1864 Vic., Australia) m.(1884) William Roberts
Birth: Robb Elizabeth, mother Mary Ferguson McKnight, father Thomas, 1864 Smyt. dist. Victoria.
https://www.irishgenealogy.ie/files/civil/marriage_returns/marriages_1884/10918/5988627.pdf