pseudoswede

1. Does this phone number belong to mobile phone provider? If yes, then T-Mobile allows for unlimited calls/text when utilizing wifi-calling. Otherwise, receiving phone calls is free (you will get charged if someone leaves you a voicemail, so you may want to consider alternate solutions), and outgoing calls cost $0.20/min (I think). I believe sending/receiving text message is also free. You also get free slow data in Australia. You can also activate T-Mobile DIGITS and make/receive unlimited phone calls and texts using the T-Mobile DIGITS app on a computer or another phone. The caveat is #2 below.
2. This move is full-time, correct? (i.e., you aren't spending six months in AU and six months in the US every year) If yes, then it gets a little trickier because T-Mobile has the right to cancel your plan if you don't spend the majority of your time in the US.
3. Do you need this specific phone number? If yes, consider porting your number to Google Voice. Then you can use the Google Voice website to make/receive phone calls and text messages, or you can install the app on another phone and make/receive phone calls and text messages using the other phone's data plan, or you can forward all calls to your Australian mobile phone (I believe it costs $0.01/min).
4. Also consider porting your phone number to (or just getting a new phone number from) Google Fi. Calls from AU to US are free over wifi (otherwise $0.20/min), and texts are free. You can choose either the cheap plan ($10/GB of data) or unlimited data. I believe there is also technically the same kind of "residency restriction" like in #2, but, again, I've never heard of anyone's account being deactivated because of it. (My guess is that if you use a ton of data where it costs Google more than your monthly plan cost, they will deactivate it.)
5. You could also port your phone number to a super cheap pre-paid US mobile phone plan and forward all calls to a Google Voice number (and utilize the stuff mentioned in #3).