I imagine Australia would continue to provide military support for the US, yes.
Your original point (slightly modified just now) is that this somehow sends a signal to NK and/or China. It doesn't. There is no increased threat of action regarding either NK or China's expanding maritime presence because both NK and China know that military action against them is a hugely different proposition. Indeed, NK has used the strike as justification for their nuclear weapons program (of course, they're unhinged depots running that country, but still, that's how they spin it).
The current movements that you have mentioned is posturing. Unless Trump intends to entirely wipe NK from the face of the planet, any attack would result in massive SK casualties resulting from artillery fire. Even if only 10% of NKs artillery works and fires, it will be devastating. They also possess the ability to strike Seoul and have a massive standing army and, again, even if only a fraction are effective and even if for only a relatively short period of time (they definitely lack supplies) they would cause huge SK casualties. On top of that, they undoubtedly possess nuclear weapons and they are insane enough to use them.
China, of course, is a major nuclear and conventional military power and whilst they lack the force projection of the US, the US is in no position to start a protracted engagement with them in their backyard, quite apart from the nuclear risk. Mattis is orders of magnitude smarter than Trump and most of his other advisors, and for that we can all be thankful. He's never going to let Trump do anything stupid regarding NK or China, so we are all safe on that front. Of course, if Trump ever dumps him, then there could be issues, but I expect you would then see Congress block any insanity.
The Syrian strike was measured and, as such things go, reasonable. It does nothing in terms of setting expectations for other matters, no matter how much you want it to show that Trump is "strong" or "tough". That strike has Mattis' hand all over it. He is a student of history and military philosophy combined with extensive practical experience. He's thoughtful and understand the true nature of strategy.