Apple Watch series 7

Probably not. You need to have an eligible cellular service plan with a supported carrier. Your iPhone and Apple Watch must use the same carrier, and you must be within your carrier's network when you set up cellular on your watch. To see which carriers support the watch in Australia, see:

Apple Watch - Carriers - Apple

A cellular watch bought in the US will only function in North America,Canada,Mexico and Puerto Rico anywhere else it will function as a GPS only watch.