First of all, not any child born abroad to a US citizen parent is a US citizen. Only children whose parents meet the conditions to transmit US citizenship to children born abroad are automatically US citizens at birth.
From what you’ve described in comments, you met the conditions to transmit US citizenship to your daughter at the time of her birth, and therefore she is already a US citizen. However, adjudicating her citizenship requires a time-consuming examination of the evidence of your periods of physical presence in the US, and immigration officers at a port of entry are not in a position to adjudicate that. And from their perspective, either she is a US citizen or she is not; if she is not a US citizen, she can enter on her foreign passport; if she is a US citizen, she has an absolute right to enter the US and cannot be denied entry; so in either case, they would let her in.
There was a similar question here about someone who born abroad who believed he had US citizenship at birth, who had already applied for a US passport but it has not been approved, who asked if he can still travel to the US on his British passport in the meantime. (In your case, you have not yet applied for a US passport for your daughter, but otherwise the issues are similar.) 7 FAM 085(b) seems to say that someone who is unable to unwilling to prove their US citizenship status can be considered an alien for the purposes of issuing a nonimmigrant visa, and that a nonimmigrant visa can be issued to someone prior to a final determination of the person’s US citizenship.
(In your case, your daughter would probably visit the US on the Visa Waiver Program on her Australian passport, for which she would get an ESTA, not a visa, but the passage probably applies to VWP visitors too.)
Regarding the US law that requires US citizens to enter and exit the US bearing a US passport, there is currently no penalty for violating this law.
Credit:stackoverflow.com‘