Is ir true Australia is going to remove him as monarch?
Whether they will actually do it, next term, (assuming they are re-elected) - I'd say it's likely, but far from certain, that they will. Will it pass? That's a very different question.
Changing Australia's constitution can only happen under strict conditions laid down in the constitution. And getting rid of the monarchy would require a change to the constitution.
We actually had a referendum on this issue back in 1999.
Now, for a referendum to pass, it needs to pass two thresholds.
(1) It must achieve a majority across the entire country.
(2) It must also achieve a majority in a majority of states.
Australia has six states, so a referendum to pass, it needs the national majority, and a majority in at least four of the six states - the idea behind this second criteria is that when Australia federated as a single nation in 1901, New South Wales and Victoria were much more populous than the other four states (they still are, really) and the less populous states feared they'd be almost irrelevant if NSW and Victoria wanted to change the constitution.
The 1999 'Republican Referendum' (referred to that way because of the idea that Australia would become a Republic if the referendum passed) failed to meet either criteria.
The vote across the entire country was close to 55-45 against the idea. (54.87 - 45.13, in fact).
And it also failed to pass in even one state.
The closest it came was in Victoria, which is generally regarded as Australia's most left-wing state, where the vote was 50.16 - 49.84 against. The furthest away was Queensland where the vote was 62.56 - 37.44.
This was all despite the republican movement believing for most of the decade beforehand, that they would easily win.
Why did it fail? First of all... opinion polls and similar nearly always seem to overstate the 'progressive' point of view (and in Australia, republicanism is more of a progressive idea, than a conservative one).
Secondly, it's often been argued that a lot of people who support the principle of Australia becoming a republic did not like the model that was going to be adopted in 1999 (basically we would have had a President elected by Parliament, and most republicans seem to have wanted some form of direct election by the people).
Anyway... that's the history.
What will happen now?
As I say, I think there is a good chance that if Labor is reelected, they will hold a republican referendum in their next term. It's not certain, but there's a decent chance.
But will it pass?
It's true that King Charles III isn't as popular as his mother, Queen Elizabeth II was. But I actually do think he's more popular and respected than the republicans realise. And there's also a lot of people who understand this really shouldn't be about the popularity of an individual monarch, but the stability of the system.
Our current system has given us one of the most stable governments on earth for well over a century now and that's not something will lightly throw away - even if they dislike the system in a theoretical sense.
A lot will come down to the model that is presented to the people - if any. I think Labor would like to try and avoid having a model if they can (that is what they are trying to do with their 'Voice to Parliament'). Basically arguing that they want people to vote for the principle, and sort out the details later. I don't know if they'll be able to get away with that approach, but if they do, they might get a majority vote - but then we could end up with a mess like that seen in the UK recently over Brexit - where people voted for the principle and hardly anybody seems to like what actually emerged at the end of the process.
If Labor comes up with a model that has widespread support, I think there's a decent chance it will pass.
But even then - we run into the fact that Australians, historically, rarely vote for constitutional change. 44 'Questions' have been put to the people since 1901, 44 attempts to change the constitution. 8 have passed. 34 have failed. Of the ones that have passed, most have had overwhelming public support (at least 70% of people voting for the change) and most have also come just after a serious national crisis that made the case for change obvious. Even though, I would say it's likely the idea of change has majority support in Australia, I'm not convinced it has the type of majority that is needed to actually change - it's that 'majority in a majority of states' thing. We've had another five referendums where the national majority was achieved (from 50.30 to 62.22) but which failed because fewer than four states voted for it.
I think we could very easily end up with a situation where a new republican referendum would get the national majority, it would definitely get a majority in Victoria, and probably in New South Wales. But the other four states... the republicans would have to win two of those, and it's honestly difficult to see which two they could be reasonably sure of. It's not impossible, by any means. But if I was a betting man... I'd say the odds are currently against it.
Also bear in mind that in Australia, voting in referendums is compulsory - so a lot of people who generally don't express their views are forced to do so... and historically this silent group has tended to vote against change without a very good reason. Why fix what isn't broken? They'd have to be convinced any change is worth risking a stable system. Even when they are not a big fan of that system.