Image courtesy of http://invisibleaustralians.org these images are part of the archival record documenting government regulation of non-white Australians. The authors of that site state:

In the early twentieth century Australia defined itself as a white man’s country, yet the reality was something different. As well as Indigenous Australians, there were many thousands of non-Europeans, including Chinese, Japanese, Indians, Afghans, Syrians and Malays.

These are the Invisible Australians – men, women and children who, because of the colour of their skin and the homelands of their forebears, found themselves at odds with the nation’s claim to be white. They faced discriminatory laws and policies designed to deny them their place as Australians.

Because of this, there are extensive government records documenting their lives. The Invisible Australians project will use biographical information found in the records to link together their lives, revealing the real face of White Australia.

"Anti-native" provisions 

1901 The racist beginnings for australia in the white australia policy

The formal White Australia Policy is charted from 1901 at the beginning of Federation - although difficulties of race were evident in the Colonies before. The last two Federal Acts passed in 1901 were the Pacific Island Labourers Act 1901 and the Immigration Restriction Act 1901. 

Section 8 of the Pacific Island Labourers Act 1901 made it clear that Pacific Islanders were tolerated while working but were to be expelled by 1906:

8.-(1.) An officer authorized in that behalf may bring before a court of summary jurisdiction a Pacific Island labourer found in Australia before the thirty-first day of December, One thousand nine hundred and six, whom he reasonably supposes not to be employed under an agreement; and the court, if satisfied that he is not and has not during the preceding month been so employed, shall order him to be deported from Australia, and he shall be deported accordingly.
(2.) The Minister may order a Pacific Island labourer found in Australia after the thirty-first day of December, One thousand nine ,hundred and six, to be deported from Australia, and thereupon he shall be deported accordingly.

The provisions against race that were the foundation of the White Australia Policy were stated less obviously in the Immigration Restriction Act 1901. Non-whites (and others) were to be excluded by the application of a written dictation test in any European language. This test established the first category of prohibited immigrants set out in section 3:

3. The immigration into the Commonwealth of the persons described in any of the following paragraphs of this section (hereinafter called" prohibited immigrants") is prohibited, namely :-
(a) Any person who when asked to do so by an officer fails to write out at dictation and sign in the presence of the officer a passage of fifty words in length in an European language directed by the officer

The prohibitions on immigration were subject to some exceptions and some non-indigenous, non-white persons were already settled and established in Australia. For information about what it was like for non-indigenous, non-white persons living in "White Australia" see Invisible Australians

The race provisions affecting voting in australia were part of federal law from 1902 

The right to vote for certain men and women (who were British subjects in Australia) was put into federal law in the Franchise Act 1902However, section 4 made it clear that British subjects who were non-white were excluded from the vote:

...No aboriginal native of Australia Asia Africa or the Islands of the Pacific except New Zealand shall be entitled to have his name placed on an Electoral Roll unless so entitled under section forty-one of the Constitution. 

Removing the anti-native provisions (but not for Indigenous Australians)

Later, in 1924, the Electoral Act was further amended following pressure from the UK to remove the 'anti-native' restriction in section 4 to allow naturalised persons and those born in India to vote:

Section thirty-nine of the Principal Act is amended by omitting from sub-section (5.) thereof the words" unless so entitled under section forty-one of the Constitution" and inserting in their stead the words "unless-
(a) he is so entitled under section forty-one of the Constitution;
(b) he is a native of British India; or
( c) he is a person to whom a certificate of naturalization has been issued under a law of the Commonwealth or of a State and that certificate is still in force, or is a person who obtained British nationality by virtue of the issue of any such certificate".