A couple of random thoughts which may (or may not) be helpful, no real evidence, just more lines of enquiry. Some of it taken from on-line trees (which I haven't check thoroughly!) Some of it you probably have already
According to the information on the site given by mclachlan
http://www.bellsite.id.au/helen_tree/HTMLFiles/HTMLFiles_11/P8191.htmlthere was at least one other family relative in Australia:
Samuel John LATHAM, b 1857 (cork Ireland), d 1933 Kyneton, Victoria. Samuel married Margaret MCHUGH in Victoria (Kyneton according to his wife's obit) in 1881 and had children with her in Victoria in the 1880/90s, so he must have arrived before 1881. However I can't see his arrival. Most of the children seem to have been registered in Kyneton.
Samuel's death notice shows that he died in Kyneton
http://trove.nla.gov.au/ndp/del/article/11688770Obit for his wife, Margaret d Kyneton, 26 February 1917
http://trove.nla.gov.au/ndp/del/article/129584811Kyneton is about 90k north of Melbourne.
I note that
Sarah LATHAM and
Andrew WRIGHT were married at Echuca, Victoria, March 1873 so Aunt Sarah had been in Australia for at least 11 years before the children came to her. Sarah and Andrew's children were registered at Moama which is just over the river from Echuca. They had been in Moama for their last child's birth in 1881 and were in Hillston by 1891 (death of a child).
I mention these items to show the connection to Victorian records and I would have thought it likely that the children entered via Victoria. The Riverina district is an area mostly in NSW but due north of Melbourne. Historically connections to/with Victoria have been almost greater than to NSW, although, of course, it's mostly actually in the state of NSW. The river Murray is the border between Victoria and NSW and there are many towns such as Echuca/Moama which are only a bridge apart but administratively in two different states. I see also that Andrew WRIGHT's family lived in Victoria so
Sorry - this has probably been s diversion from the main topic.
I wonder if the children came in the care of another family/couple and were, perhaps, listed on the shipping records with a different surname. I did try a trawl through the PROV unassisted immigration lists for a "Julia" whose age and arrival date might have been a possible but came up with nothing.
As I said - pure speculation and they may well have arrived through NSW, so not much help at all!
Judith