I think that address in that advert for her father would be using a commercial business perhaps as though it had a side line offering a bit like a poste restante address ...
City of Sydney Assessment Books. Macquarie Ward, 1911.
King Street
Number in Rate Book : 9019
No. of House : 127
Name of Person Rated : Chapman & Hazelwood
Name of Owner or Landlord of Property : Australian Mutual Fire Insurance Coy
House, Warehouse or Shop: Chambers
Brick, Stone Wood or Iron : Brick & Stone
Slated, Shingled or otherwise : Slate
2 Floors
14 Rooms
Gross Annual Value £456
Nett Value fixed by Quarter Sessions £411
https://archives.cityofsydney.nsw.gov.au/nodes/view/1842002#idx2519416 Sands Directories 1910 Sydney (and years before and after then too)
Chapman & Hazlewood, Real Property and Financial Agents, Estate Managers, 127 King Street.
JM