Unfortunately, as far as I know, no popular effective altruist charities are registered in Australia yet, so I don't think this is possible to do there.
Also note that even if there were a tax-deductible EA charity in Australia, it's not at all clear that your donation to the Australian charity would be tax deductible if your actual purpose was to donate via a swap to a non-tax-deductible charity.
Unfortunately, as far as I know, no popular effective altruist charities are registered in Australia yet, so I don't think this is possible to do there.
Also note that even if there were a tax-deductible EA charity in Australia, it's not at all clear that your donation to the Australian charity would be tax deductible if your actual purpose was to donate via a swap to a non-tax-deductible charity.