Yes, vaping is legal in Australia.
You can purchase and consume vapes or e-cigarettes in Australia provided they do not contain nicotine. Currently, you can only get nicotine e-liquid if you have a prescription to use it as a nicotine replacement product.
It is illegal to own, buy, or consume e-liquid in Australia without a prescription.
In Western Australia, it is illegal to sell a vape and in some other states, it is illegal to sell vapes or e-cigarettes which resemble actual cigarettes.
Vaping nicotine in Australia carries penalties of up to $45,000 and/or two years in prison.