Here are are some tips from Trove (National Library of Australia) for searching diaries, letters, archives.
Search personal and organisational archives, including diaries, manuscripts, letters, business records, photographs, posters, pamphlets, ephemera using Trove.
Other places to search for government records (including births, deaths and marriages) try:
“National Archives of Australia;
“State Records Authority of New South Wales;
“State Library of NSW;
“Public Record Office Victoria;
“Queensland State Archives;
“State Records Office of Western Australia;
“State Records of South Australia;
“Tasmanian Archive and Heritage Office;
“Northern Territory Archives Service;
“ACT Territory Records Service.
Other major archives:
“University of Melbourne Archives;
“Noel Butlin Archives Centre.