A search of the Birth Index's for South Australia for the years 1858 - 1872 doesn't show any Dorathy Rose Menzels born in South Australia. You can search yourself using the following website: www.genealogysa.org.au. I can't find any reference to a Lydonsh in Google maps or Wikipedia either.
Was Menzel her maiden or married name and do you have any further informaton such as wedding date?