djtech is right – American Express is your best way to accumulate Emirates Skywards miles but be aware that even AmEx Ascent points convert to Skywards at a 4:3 rate – so even a 100,000-point AmEx signup bonus will only net you 75,000 Skywards points when converted. And the rate will reduce further after April 14.
Two strategies that might just possibly work for you to accumulate the extra 135,000 points are…
Put a couple of hundred thousand dollars worth of expenses, or business expenses, on your AmEx card and accumulate the extra points through spending. (this will only work if you’re uber-wealthy or a business owner).
Get your spouse or partner to _also_ apply for an AmEx card, and set up an Emirates Skywards My Family account to (sort of) pool your points. (This will only work if you have a spouse or partner).
If you have a very high income and/or family who are willing to help out, 210000 points before September is doable – but only barely. If you’re earning an average Australian wage or thereabouts, I don’t think you’ll be able to make it.