Travelling from USA to Australia [closed]

If your Permanent Residency Visa is for Australia, not an equivalent for the USA like I'd originally assumed, then you just need to make sure you have a "valid travel authority" for your visa. In general that's automatic as part of the visa.

If the visa was referring to the USA, as Indian nationals are not able to get Electronic Travel Authority or eVisitor visas you will need to apply for a Visitor visa.

The last link provides the details, but in summary you need to apply for the visa outside Australia and meet health and "character" requirements, i.e. not been arrested recently.

You will need to make sure you bring the following information to be able to return to the USA:

If you travel out of the U.S. while you are in H status, you should have the following documents in order to be re-admitted to the U.S.

Passport valid 6 months into the future
Letter from department Chair or Dean confirming current employment in same position described in his / her H petition
Recent check-stubs proving current employment at employer sponsor
Copy of complete H-1B petition filed with the CIS Valid Form I-797 H Approval Notice (Request the top portion of this form from the Office of Visa and Immigration Services. Please return this to the Office of Visa and Immigration Services upon your return.

If appropriate, original J-1 home residency I-612 Waiver Approval Notice (only applies to former J-1 holders who were subject to the two year home residency requirement)
Valid H visa for re-entry to U.S.