Texting. Google Voice will let you port your US Mobile number to them for $25 (sign up before you leave the US or before you discontinue cell service). They will give you free texting to the US or Canada. Their client uses data and needs to be downloaded from the US App Store (or your OS's equivalent). Google Voice will not forward the number abroad, but you can make free VOIP calls using Talkatone (iOS) or GrooveIP Android. They use data. Some Australian VOIP carriers block VOIP on their prepaid plans.

If you want to forward the number to Australia, you need someone else or a PBX switch. For example, I pay 2.4 cents a minute to call Australian mobiles. You need to find the right carrier.

If you just want to take the calls over the internet, Google Voice with Talkatone or GrooveIP is fine. You can text message over data. You can also possibly make a call over 3g/4g depending on the connection.