In the US, licenses are issued by the individual states. Tourists can typically drive for a limited time using their non-US licenses. However, I'm a retired attorney and I've never heard of any state accepting a non-US license as a method to bypass any part of the state licensing procedure.
Each state's Department of Motor Vehicles maintain on-line web pages where you can research state requirements for licensure. I just checked California and Nevada, which behave in the manner I describe above — that is, no credit is given for non-US licenses.
IOW, having a non-US license is irrelevant, and an adult applicant for a US state drivers license must begin the state's application process from the beginning. (See 8-10-18 edit below about license reciprocity between France and the US states of Texas, Oklahoma, and Arkansas.)
In the US, applicants must pass both theory testing and on-the-road driving testing, and must provide a licensed and insured vehicle in which to be tested. For those over 18, there is usually no minimum time period in a restricted license class, one may submit to testing right away. Remember too that states issue licenses to their residents, and you'd have to demonstrate that you are a resident.
All in all, then, your plan of using your current Australian limited license is not going to confer any advantage on you in applying for a US license.
If you did obtain a US license, I have no idea if holding a US license might allow you to directly obtain a Full Open license in Australia. That's a question for someone familiar with Australian law.
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Edited 8-10-18:
Thanks to @MJeffryes, who has commented below that France has reciprocal license-exchange agreements with the US states of Texas, Oklahoma, and Arkansas. Exchange is possible there bi-directionally upon proof of residence.
Edited 9-4-18:
This SE.StackExchange item says that the state of Pennsylvania has similar reciprocity.
I'm not aware of any other country/US state combinations that allow exchange.
