There are so many points being said that are inconsistent with international law and specifically with UNCLOS that it warrant a response.
Japan won't. Australia ? Maybe, like fleet support and some "lookouts" near its western coasts.
US ? Yes but depends on how much India is ready to escalate.
First up, QUAD is not a military alliance. It is a quasi formalized network of nations with like minded purpose and resolve regarding the maritime domain. Its purpose ultimately is deterrence against any nation(s) that act outside of established international law.
Any conflict arising between nations is not because of the presence or absence of an alliance but a formal declaration of war consistent with the law of international armed conflict. As established by UN convention, every country has the right to exercise self defense. Therefore any country be it Japan or Australia will have to make the same determination. Is it under threat and does it need to exercise self defense as a sovereign nation in response to such threats? The question therefore you need to not only ask but address is what kind of threats would rise to a level that warrant armed conflict involving such nations.
Making statements that country X would be involved or not in a conflict without setting out the conditions is rather superflous in reasoning.
The major issue is that China won't be "aggressive" in the Indian Ocean. You have to define "Aggression". The Indian Ocean belongs to Maldives, Sri Lanka, Indonesia, UK, Myanmar as well as a lot of African nations.
The Indian Ocean just like the South China Sea does not belong to any country. It is well established law of the sea for centuries which subsequently became embedded and formalized within UNLOS that international waters is global commons subject only to 12 nm of territorial sea entitlement for coastal states. The concept of EEZ was introduced as a compromise between coastal states and maritime sea power nations at that time such as the US, Russia and UK et al.
The Indian Ocean is dominated by India because of proximity and not because of legal standing. As such it has advantage in any conflict with China because of its location. However any actions at sea by India will necessarily be an extension of an already existing conflict in play and not something conducted in isolation. India cannot interdict or conduct blockade at sea against Chinese vessels under international law unless both countries are at war or it is sanctioned by the UN.
Esclation can only happen in Indian Ocean if China intrudesinto and conducts "activities" in Indian EEZ. Otherwise China can do whatever it wants in the Indian Ocean like other nations.
If India wants to "own" Indian Ocean, then it must start doing what China is doing in the SCS. Construct Islands, Defend it, stake claims and be ready for any escalations. Otherwise, Indian Ocean won't belong to India.
Such reasoning is almost comical. The reason why the world has generally been at peace since WW2 is because there are a set of international laws to govern country behaviors. It would be chaos if countries decide to take action not based on international laws but that might is right. That was the policy of Nazi Germany and Imperial Japan.
There are no two sets of rules in international law that somehow it applies to the Indian Ocean but not to the South China Sea. You cannot create artificial islands and claim territorial sea out of it. UNCLOS set it out clearly and that was validated through arbitration. China's position is not based on legal standing but that might is right. The international community does not recognize China's claims in the SCS and that is where we are at the moment. We either have a continuing stand off or WW3 to resolve it just like with Nazi Germany or Imperial Japan.
