Of those _nation states_ still in existence, New Zealand was the first to give women the vote, also in 1893.
(It's worth pointing out as well that the right was losing its grip on Australasian politics in the 1890s --- Queensland had the world's first elected labour/socialist/working class government in 1899 -- and since Australasian women tended to vote conservative at the time, introducing women's suffrage was a vote winner for tories.)
----- Original Message ----- From: Bill Bartlett
> I believe the colony of South Australia had universal suffrage prior to
Australian federation (1901).
> Aborigines lost the right to vote, indeed they lost citizenship entirely,
upon federation and did not
> regain rights until 1967. This was originally due to a fear in the eastern
states that Western Australia in > particular, with its large aboriginal
population, might abuse the system.
> You might want to nit-pick that South Australia was a British colony prior
to federation, rather than a
> "state", but it had its own parliament and was substantially
self-governing. As self-governing as
> Australia after federation anyhow.