I am a Pakistani national who is migrating to Australia in December 2016 on State sponsored business visa through the government of Australia. I intend to visit the USA in April 2017 and return to Australia.
Can I apply for a US visa from Australia, or do I need to apply from Pakistan?
Details of how to apply for a nonimmigrant visa for USA from Australia are available at the U.S. Embassy & Consulates in Australia site.
There is no mention there that the applicant must be an Australian citizen to be able to use that service. So, yes, you may apply for a US visa from Australia and, no, you do not need to apply from Pakistan.