US citizenship for an Australian dual-national while on 90 day visa in America?

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 return to customs after arriving.

The premise of the question is that a US citizen has been admitted to the US under the visa waiver program and subsequently receives a US passport. In that circumstance, the other answer is correct, because as a matter of law, a US citizen cannot have any immigration status other than that of a US citizen. In fact, a US citizen who has been admitted under the VWP doesn't even need to get a US passport to remain in the US; any evidence of US citizenship will do.

The premise, however, is somewhat questionable. In other words, this sentence could be incorrect:

My daughter will be in America with me on the 90-day visa waiver program.

In fact, she might not be admitted on that basis. If your daughter's citizenship becomes apparent to the passport officer, she should be admitted as a US citizen even without a US passport. The officer could discover that your daughter is a US citizen in one of at least two ways:

1. You mention it when you approach the passport inspection desk, or
2. The officer finds a record of your daughter's passport application or CRBA application after scanning her Australian passport.

The second possibility is particularly likely if either application included your daughter's Australian passport number, but even if it did not, it's possible to match the records based on other biographical details, such as name and date and place of birth.

If this happens, the officer could give you a lecture about your daughter needing a US passport (or maybe not, since you've already applied for one). Then the officer should waive the requirement of 8 USC 1185(b), admitting your daughter as a US citizen. In that case, of course, there will be even less reason to do anything with regard to any record of her admission as an Australian citizen, because there would be no such record.

To prepare for this possibility, you may want to bring copies of the evidence you submitted with the CRBA application, in case the application hasn't yet been approved by the time you arrive in the US and the officer wants to have an independent look into the question of your daughter's citizenship.

If you are saying

1) the child will enter using an Aussie passport / visa and

2) while you are there the child will receive in the mail the birth record and also a US passport

Yes, it's all a non-issue. Do nothing.

Once the child receives the US passport, forget everything, she can stay in the US. (If she likes junk food :) )

Nothing to do or worry about there.