From correspondence sent to Joan, an Ancestry contact:

I took a look at emigration records on findmypast.com. I found a Mrs Mary A. McElroy, age 68, of 14 Woodhall Ave, Egremont, Cheshire, who took ship to Melbourne, Australia on the P & O ship Beltana on 7 Aug 1924 out of London. Next to her name is the letter W, which I presume stands for widow. On the same ship were also:
James MCELROY, a painter, 42
Mrs Jane MCELROY, wife, 40
Lorna E MCELROY, 10
Evelina L MCELROY, 9
Gordon S MCELROY, 3
James was on ticket 1191. The rest were on ticket 1190. All had England as their country of most recent residency.

I presume that James, the painter is Mary's son. There's a slight discrepancy in his age (he was 17 at the 1901 census). Nonetheless, this could be the family you seek.