I got married to an Australian citizen April of 2017, and moved to Australia officially in June of the same year. I am unsure of how to proceed with my taxes as I don’t even know how I am going to get my W2, and he does not have a SSN.
For your W-2 you should have provided a change of address with the US Postal Service and contacted your previous employer's with your new address. Employers have until January 31, 2018 to provide a W-2.
When using TurboTax for your personal information you will be asked for your resident state. In the dropdown for states, scroll to the bottom of the list and select Foreign or US Possession. Where asked if you lived in any other states, select the state you moved from and the date you moved to Australia.
If you are a US citizen and your spouse does not have a Social Security number or an ITIN and you are not applying for an ITIN with the tax return then you can only file your tax return as Married Filing Separately. Using TurbotTax, where asked to enter the spouse's Social Security number enter 999-88-9999. You can only print and mail your tax return, it cannot be e-filed. When you print the tax return erase the Social Security number for your spouse and manually enter NRA for non-resident alien.
See this TurboTax support FAQ for the procedure to print and mail a tax return using the online editions - https://ttlc.intuit.com/questions/1944348-how-do-i-print-and-mail-my-return-in-turbotax-online
Your spouse would only need to report their income if you were filing your tax return as Married Filing Jointly, applying for an ITIN with the tax return and you would be providing a statement with your tax return that you want your Nonresident Alien Spouse Treated as a Resident. See IRS Publication 54 Tax Guide for U.S. Citizens and Resident Aliens Abroad pages 6 and 7 - https://www.irs.gov/pub/irs-pdf/p54.pdf
Go to this IRS website for ITIN information - https://www.irs.gov/individuals/international-taxpayers/general-itin-information