Yes you can, but you will need to confirm that it is the correct size.
The first thing you should do is check to see what type of SIM you have with your current device. The most common sized SIM cards that are used today are 'nano' and 'micro' sim cards.
Each device on the OzMobiles page will have the SIM type listed beneath in the device specifications. Once you determine if the SIM is the same size, you can use your current sim with your newly purchased device.