For a possible Australian connection, have a look at this family:
1891: 116 Breck Rd, Walton on the Hill, Liverpool
Edward Welsh Head Mar 37 Tobacconist Lancashire Eccles
Antoinetta do Wife Mar 24 Lancs Manchester
Wm Henry do Son 2 Manchester [William Henry Welsh mmn Delungs, Sep qtr 1888 Chorlton]
Harold do Son 1 Liverpool [Harold Welsh mmn Bellungo, Dec qtr 1889 West Derby]
Edith Violet do Daur 1mo Liverpool
1901: 116 Breck Rd, Walton on the Hill, Liverpool
Edward W Welsh Head Mar 48 Tobacconist & confectioner Lancashire Eccles
Antonietta do Wife Mar 34 New South Wales
William H do Son 12 Manchester
Edith A do Daur 10 Liverpool [Edith Antonietta Welsh mmn Delungo, West Derby Jun qtr 1891]
Florence H do Daur 4 Liverpool [Florence Hilda Welsh mmn Dellings, West Derby Sep qtr 1896]
+ 1 female servant
1905: Birth reg of Doris Ida Welsh mmn Delungo, West Derby Sep qtr 1905.