I'm no expert regarding eligibility for welfare but this seems to make it fairly clear the OP would not be eligible for a Low Income Health Care Card until he has been in Aust for 104 weeks. It is highly unlikely a new arrival would be granted an exemption.
My own opinion is that if you can afford to migrate you shouldn't be looking for welfare as soon as you arrive.
[h=3]Residence requirements for the Low Income Health Care Card[/h]To be eligible for a Low Income Health Care Card you must satisfy residence requirements.
You must be living in Australia and:
have Australian citizenship
hold a permanent visa
hold a special category visa, or
hold a partner provisional visa subclass 309 or 820, an interdependency visa subclass 310 or 826, or a temporary protection visa
You must also:
be physically present in Australia on the day you lodge your claim, and
continue to meet the residence requirements for as long as you hold this card
Newly arrived residents generally have a 104 week waiting period, with some exemptions.
http://www.humanservices.gov.au/customer/services/centrelink/low-income-health-care-card