I'm sure the Frigate has Rules of Engagement as to when a conflict starts they won't automatically jump in, but instead wait for orders from a higher Australian chain of command.
Say for instance out of nowhere this US carrier strike group, patrolling in the Pacific, is attacked without any provocation by China. Obviously the Frigate would defend itself and the US ships in the group.
But now let's say, this US CSG is sailing towards the Taiwan strait or some other contentions waters near China during times of high tension between China and US and the world can spot the precipitous of a conflict, I'll bet that you won't find the Frigate sailing with the CSG towards this conflict.
Allies embed the ships with US CSGs all the time to train with the US tactically, but on a strategically level, it means nothing.
Just because they sail ships together in times of peace doesn't means they will fight together. .
My understanding is that this is a strategic commitment supported by both political parties in Australia. You don't see this questioned by either of them.
It's a frigate permanently stationed and embedded with the carrier strike group in Japan.
If in time of crisis, Australia pulls the frigate out, the entire US-Australia alliance comes into question. And for the next 10+ years, the US does have enough military strength to secure Australia's sea lanes from China. But in 15years, we may see Australia reevaluate it's position, depending on what China's military capabilities look like.
And if a US carrier strike group comes under attack, incoming missiles will not discriminate between US or Australian shops.
So Australia definitely doesn't want to get into a conflict, but may be compelled to, because of its alliance with the US.
From the Chinese perspective, it isn't interested in a conflict either. Domestic economic development and a prosperous hitech economy is still the top priority.
An economy which doubles in size over the next 12-15 years is achievable given the experience of the other East Asian economic tigers. That means a lot more Chinese economic and military influence.