Mumsnut
Mostly No, because EQ2010.s9 defines what characteristics count as "race" for the purposes of determining if somebody has the protected characteristic of race for the purposes of EA2010. Kind of Yes, but not actually self-ID for the person who might have been discriminated against, rather a kind self-ID via perception for the person who has been accused of doing the discriminating (basically if somebody discriminates against somebody else because they think they are of a particular ethnic background, but the person being discriminated against isn't, that still counts as discrimination).
(ss1 - ss4):
(1) Race includes—
(a) colour;
(b) nationality;
(c) ethnic or national origins.
(2) In relation to the protected characteristic of race—
(a) a reference to a person who has a particular protected characteristic is a reference to a person of a particular racial group;
(b) a reference to persons who share a protected characteristic is a reference to persons of the same racial group.
(3) A racial group is a group of persons defined by reference to race; and a reference to a person's racial group is a reference to a racial group into which the person falls.
(4) The fact that a racial group comprises two or more distinct racial groups does not prevent it from constituting a particular racial group.
Of course, this covers everyone because everybody has a colour, everybody has an ethnic or national origin, most people have a nationality, but the reasons the definitions are included in the act is so that the Court can judge if somebody has been discriminated against because of one or more of ss1 qualifiers, and if they have then they've been discriminated against as a result of race.