I think your Dellaways are probably connected to mine. My grandmother, Amy Rose, was the eldest of 11 children (she was born in 1898) in a place with a curious name: Jolly Bleachings in Croydon. When I looked at the 1901 Census, there were a couple of Dellaway families living in this street, road or whatever it was (it has obvious connections with laudering).
My grandmother always said that the Dellaway family had connections in Cork, Eire. I never met any members of her family because by the time I was born she had lost touch with them. However, she did mention brothers and nephews who won scholarships to Whitgift School in Croydon and you might like to research that.
I am afraid that I cannot add much more than that, except when I looked at the page on the census there was a Mary Dellaway but obviously this was after your family had gone off to Australia.
Best wishes, P. Vivien Pegram