Since you're making a consular record of birth abroad, presumably your daughter was a US citizen at birth. She can stay in the US as long as she wants. While she will get a stamp admitting her for 90 days in her Australian passport, this doesn't apply to her, as she is a US citizen.
Technically speaking, as a US citizen, she must enter the US using a US passport. However, breaking this law has no real penalty. See this answer, for an explanation of what could happen at the border.
So no, she neither needs to fly back to Australia, nor visit customs after arriving.