Can my wife stay beyond her visa expiration without jeopardizing her approval of our I-130 petition?

The legal consequence of her we failure to leave the US will depend on the status of the petitioner and her relationship to such person. If for instance, you are her husband and you are a US citizen, then, her failure to leave may not have dramatic consequences. otherwise, she may not be eligible to get her green card. You should consult with a lawyer

The problem with your case is that you filed I-130 while your wife was still in Australia providing Australian address. As such, upon approval the I-130 will be sent to National Visa Center for Consular Processing. Another issue is that your wife entered under VWP. If she stays for adjustment of status here the USCIS may raise dual intent issue at the time of the interview and deny your wife's adjustment. In this case she won't be able to seek judicial review of the denial because of her initial entry under VWP. Before you do anything further seek a formal legal advice from an immigration attorney.

As the spouse of a US citizen, your wife is eligible to apply for permanent residency while in the United States even though she entered the US without a visa, because there is an exception for immediate relatives of US citizens. The process is called adjustment of status and the application is filed on form I-485. As long as you are able to convince USCIS that she did not have the intention to remain in the US when she entered under the visa waiver program, her application should be processed without any complications. You should submit a copy of her round trip airfare to prove that she had the intention to return to Australia to wait for the processing of the I-130 petition. If you are unsuccessful in that regard, USCIS will likely require her to file a waiver on form I-601.

She would have to file for her adjustment of status. The I-130 in and of itself does not grant status. It presumes that she will consular process for the immigrant visa once the I-130 is approved. If she does not plan to return to Australia, she needs to file adjustment of status to permanent residence in the US in order to get the green card. Please let me know if you have any additional questions or how I can be of further assistance to you in this matter.