You’re eligible to apply:
Who You Are:
• You are a citizen or eligible national of a Visa Waiver Program country.
• You are currently not in possession of a visitor's visa.
• Your travel is for 90 days or less.
• You plan to travel to the United States for business or pleasure.
• You want to apply for a new authorization ...
Countries generally prefer you to leave on the same passport you entered the country in. Of course this isn't always possible (citizenship change, for example).
The Home Affairs website notes for dual citizens:
A dual citizen is a person who is a citizen of 2 or more countries.
You become a dual citizen if you:
are an Australian citizen, are ...
ALL Australian citizens can use Smartgates at Australian airports. These are, by far, the fastest means of entering Australia.
US Citizens can also use these gates, however this isn't relevant to you as to enter using a US passport you would require a Visa/eTA which you won't have - plus you are supposed to use your Australian passport if you are an ...
You should not run into any issues. Your reasons for traveling are valid and totally covered under the ESTA program.
I would just take the precaution of bringing along documents that prove your itineraries (your stays in NY, Toronto, Vancouver, LA, and LV) along with a return flight home. This will just show the border guard that you are genuinely ...
So to update what transpired.
I managed to contact the manager of the citizenship dept at the high commission in London, and she said that they can put off the final approval until after my daughter arrives in Australia with her US passport and ETA.
So immediately after she arrived in Aus, i asked them to finalize the citizenship, which they did the ...