Don't like Australia's torture and systematic neglect of refugees in Pacific island concentration camps? Want them to end this environment of self-harm, despair, and sexual abuse and accept their responsibilities under the refugee convention? If you're Australian, you can try voting for those outcomes. If you're not, then there's really only one thing you can do: don't buy Australian.
Buying Australian goods and supporting Australian companies supplies the Australian government with tax revenue - tax revenue it spends on the torture and abuse of refugees. Refusing to buy Australian or support Australians with your business reduces that revenue. It also ensures you are not complicit in supporting these crimes against humanity.
Boycott campaigns have a mixed record. But they were successful against apartheid South Africa, and (judging by the intense Israeli reaction) are being successful against Israel. At the least, they de-legitimise behaviour and make it clear it is unacceptable to the global community. Australia's behaviour is unacceptable - and they need to know that. So, don't buy Australian, and let the companies you have stopped buying from - Arnotts, Harvey-Norman, Jacob's Creek, Holden, whatever - know about it. Because while you can't do much to change Australian government policy, they can, and will if it starts to hurt their bottom line.