These are figures from a few years ago (2015) but I'm sure the rates will be roughly the same:
'Among the top ten source countries of permanent migrants (excluding New Zealand), in this group, there were two countries with predominantly Muslim populations: Pakistan with 8,281 (4.4%) and Malaysia with 3,977 (2.1%). So the number of migrants to Australia from majority Muslim countries was
dwarfed by the number of from India 34,874 (18.4%), China 27,872 (14.7%) and the United Kingdom 21,078 (11.1%).'
Australia is in danger of being swamped by Muslims? The numbers tell a different story
So no, there's no vast immigration of Muslims. And the third highest intake was from the Philippines. Which is not Muslim as you stated, but over 90% Christian. Add those to the immigrants from the UK (predominantly Christian) and the overall influx is biased towards Christianity. Yet the percentage is still dropping.
And we have a democracy here. If anyone wants us to become communist then they can join the Australian Communist Party. They need all the help they can get. The last election they ran for was in 2010 and they got around 0.001% of the votes. So...some work to be done there. And they were going to run again in 2017 but didn't have the 500 members they needed by the Electoral Commission.
So no...we won't be Communist either.