Hello,my name is Judith. Thank you for this opportunity to answer your questions.
You have good intuition.
She cannot enter the US on a visitor status with the intention of staying and immigrating.
When she enters she will be asked a lot of questions because the inspector will see she has the visa for Australia as a student and has been out of her country for a significant period of time.
They may send her back to secondary inspection because they will want to question her about what ties she has to Northern Ireland.
She does run the risk of being refused admission and if she is administratively removed she faces a 5 year bar to coming back, even under sponsorship of her husband who is a US citizen.
If the inspector believes that she has lied it could get even worse - a permanent bar.
Often spouses of a US citizen do enter as a visitor and then spontaneously change their mind and stay and file for their adjustment.
But they are not coming here after being away from their country for a year and no longer having any ties there.
If they do things the right way they will face a separation of 6-10 months.
He will file form I-130 with the USCIS here in the US at the lockbox (PO Box)
as per the instructions.
He must include with the form a G-325A for himself and she along with 2 passport
style photos of each of them.
You can find those forms and instructions at this link
Once the petition is approved (it will take 3-5 months) he will be notified
and the petition will be sent to the National Visa Center. In
approximately 2-3 weeks they will send him a bill for the immigrant visa fee
$230 and your Affidavit of Support (I-864) $88.
Once he pays these he will receive instruction on submittin the I-864 and she
will get her instructions on begining the immigrant visa process by submitting
the DS-230 Immigrant Visa Application.
After that is received the USCIS will request her background/security check be
done by the FBI.
When the clearance on her is received her file is forwarded to the US consulate
or Embassy closest to her.
She will then receive her instructions for her medical and visa
She will be told what documentation to bring.