Err....
There's something online on the National Archives of Australia ... it could be a clue, if perhaps that co-respondent, William Larson stayed with Elizabeth...
Its the arrival in OZ, of a William LARSON in 1908, ... and his nationality was Swedish (that does NOT mean he was born in Sweden, but it would be likely) and date of birth was 2 March 1881 ... no ship's name shown, BUT there's an arrival date (in OZ) of 30 September 1908... and he was first registered at Donald (all "aliens" had to register on arrival and many had to sit a written dictation test (to make sure they were not 'coloured aliens' ... don't ask ... it was also known as the White Australia Policy. Anyways, that file at the archives, it would cost around $16.50 to have that record digitised, and there's NO reason to consider that just yet.
But, perhaps there's an outward passenger list for his voyage from "somewhere" to OZ, (probably took about 5 weeks under steam from say Southampton !) so from say July 1908 .... perhaps Elizabeth accompanied this person, perhaps he was a nephew of her co-respondent ... speculately as usual ... sorry
Search as a Guest, using keywords William Larson
http://naa12.naa.gov.au/scripts/ResearcherScreen.asp there's only 13 indexed, and the "barcode" for this chap is 6565067
Cheers, JM