TurboTax does not support Form 1040-NR or Form 1040NR-EZ. However, TurboTax partner Sprintax.com can help you decide what type of return you need to file. They are very helpful and knowledgeable.
Substantial presence
You meet the substantial presence test because you were not on an F, J or other exempt visa holder and were present in the US for more than 183 days. Since you have an H1B visa, I assume you were “engaged in a trade or business” in the US even if you did not have any US income so you will likely file a US tax return.
See Taxation of Nonresident Aliens
Dual-Status
A dual-status alien is a taxpayer who is both a US resident alien and a non-resident alien in the same tax year. Incoming US residents file a Form 1040 along with an attached Form 1040NR to show the income for the part of the year you are a non-resident. This sounds like you. Sprintax can handle those situations.
See Taxation of Dual-Status Aliens
Non-resident Spouse treated as a resident
You did not include any information about the tax status of your spouse. However a married couple can elect to file as US residents if one spouse is a resident at the end of the year and the other was not. All worldwide income would be taxable to the US and you would be eligible for a foreign tax credit for taxes paid to Australia. This is an option. Not a requirement.
See Non-resident Spouse
Learn more from TurboTax at: How should I file my taxes as a dual-status alien?
