Good sleuthing there by deeess. Julia & Joseph had another son, Paul, in Sydney in 1882.
I suspect the death of a Julia KEOGH in 1883 is the mum and that would explain why the children ended up in a children's home (except eldest Mary, who may have been working by this time, and baby Paul, probably farmed out to a wet nurse). Her parents are stated as Thomas and Mary (reg 289), which fits children's names. This death cert may reveal some clues such as her birthplace and mother's full name.
(The one in 1885 was wife of Anthony, from funeral notice). To add to the confusion there was also a Matthew KEOGH with wife Julia, though a bit later in NSW!