Don't forget your TSA fingerprinting prior to the start of class. ( You don't strictly need it for Indoc or Ground School but definitely for sim.)
https://www.thupthupthup.com/fingerprint.htm
Best to come over with your Australian medical and IPC still valid.
PRIA forms.
FAA Restricted Radio Licence
Review the FAA ATP practice exams, Gleim or Sheppardair are good.
You need to do company pre-employment drug testing. Your company will nominate a lab for you to attend.
Social Security Number. When you arrive in the US, get it asap!
US bank account, you will need one for your payroll.
Moving and living in the US depends on you and your budget. Large cities are expensive, crowded, and sometimes sketchy. Smaller towns and regional cities are cheaper but you may have to commute to work.
Much like Australia, recruiting pilots will see straight through you if you start with a new company then bail then six months later. Show some loyalty to your new employer, after all, they are paying for your E3, ATP-CTP, Type Rating (bond free) and Accommodation. Most likely you will also be paid a Starting Bonus. If you leave early, you will have to pay the bonus back either pro-rata or the whole pre-tax amount, it depends on the company. If you really only intend to stay for a short period of time it would be best not to take the bonus check (cheque) at all.
Budget enough to get yourself a car.
Expect 5-7 days of company Indoc (Induction). Ground School and sims will either be AQP or an old-school TR with a jeopardy-type ride at the end. Any training failures are permanently recorded on your ATP license. You are required to disclose any training failures if you apply for another here job in the US. It will be picked up on PRIA anyway.
Training culture is different here. Come prepared, know your flows and scans, and memorize your emergency recalls and aircraft limits. Be humble, listen and learn from your instructors. Please don't invoke any Oztronaught "we did it this way" BS and you will be fine.
If you make it through training, company dependent, expect 50 hours OE with a check airman.
You may then be placed onto a reserve schedule, or you may be able to hold a bidding line depending on the company. Either way, you will normally be paid 75 hours of credit plus per diems (tax-free) if you fly.
Good Luck!