Yes. You will pay international rates, and he will likely have to pay too since he is roaming. It would be cheaper to get him a local SIM (and maybe even a phone from here if his phone is carrier-locked).
The determining factor is the number that you're calling - not the physical location. When you call his Australian number, your call is sent to Australia to whomever is Koodo's partner network, then your cousin's network (if applicable), then routed back to you the same way. So even though he may be standing next to you, your call is going around the world and you both pay extra.