The title of this is probably a bit misleading as I didn't mean no ALP at all but instead one that is never powerful enough to get into government.
What if this occured. I am thinking here of Canada which (the 'complicating' factor of Quebec aside) is a primarlily 3-party affair; the main party, the centrist Liberals, the 2nd party the right-wing Conservatives and the 3rd party, New Democrats. The first 2 are powerful enough to form government (at Federal level), whereas the last is a powerful third party.
What is the possibility of something similar having developed in Australia in the late 19th and early 20th century? In this ATL I'm thinking that nowadays the party would form something like this: Social Democrats (Labor Left and the Greens OTL), the Liberals (Labor Right and small 'l' liberals OTL) and the Conservatives (Liberal Right OTL). The ATL Liberals would be the natural party of govt and the Conservatives ATL would be the natural opposition. The Social Democrats would a very powerful 3rd party.
What is the POD that would allow such a ATL to occur. I think that it would be quite plausible especially as nowadays the difference between Labor Right and small 'l' liberals is virtually non-existent.
I think a POD in the 1890's or very early 1900's is necesary. Perhaps more successful strikes in the 1890's which lead the unions never to feel the need to produce a party exclusive to themselves is likely.
Also any POD would require the Deakinite Protectionists not to feel so threatened by the Left, so that they choose to go into alliance with moderate social demorats (Labor Right) rather than with the Free Trade Party.