They are coasting on not doing a Kamala, yes, but the ALP also know the US is going to veto it. Having a little bit of political knowhow is better than none, but they just lost Queensland to ghouls who are trying to unilaterally ban abortion.
Australian Labor's strategy right now is to wait for the Liberals to fuck up harder. The unions were striking in the middle of Sydney in a brilliant show of solidarity and Labor largely stood by and actually did very little. Considering they're a major party in the first place due to union support, waiting on Liberals to fail isn't a foolproof strategy.
Even now Libs are drumming up support and blaming the results of their own policies when they were in power on the current ALP and what the ALP has done is basically nothing.
There is no veto for General Assembly votes, only Security Council votes. This becomes official UN policy if it passes. The issue with General Assembly votes is that there's no teeth in the organisation, there's no enforcement or consequences for not abiding by the votes, they're purely political in that regard. Except for a few things that is, Apartheid South Africa was successfully suspended from the UN entirely despite the US and British opposing it during the vote, so the General Assembly can be used to achieve things that affect the UN as an organisation if the will to do it can be found.