Neither country taxes the inheritance itself
This is the reassuring part, and it is genuinely reassuring on both sides. India has no inheritance tax and no gift tax, and the income-tax law exempts anything you receive under a will, by inheritance, or as a gift from a relative, under the proviso to Section 56(2)(x), so the Indian receipt is tax-free. Australia is the same in spirit: it has no inheritance tax, no estate duty and no gift tax, so receiving money or property, including from overseas, is not taxable income to you as an Australian resident. You do not declare the inheritance itself as income in either country.
So unlike an heir in Germany, Ireland or France, you are not hit with a tax simply for inheriting. The one thing worth noting is that a very large transfer into Australia can prompt the tax office to ask about its source, so keeping clear evidence that it was an inheritance is sensible. But there is no tax on the receipt. The tax, when it comes, comes later, and it comes through capital gains.
The trap is capital gains tax when you sell
Australian capital gains tax does not touch the inheritance when you receive it, but it does when you later sell an inherited asset, and this is where an Indian inheritance can carry a surprise. When you sell an inherited Indian property, Australia taxes the capital gain, and the crucial question is what cost it measures the gain from. The general rule is that you inherit the deceased's own cost, so if your parent bought the flat decades ago for a small sum, your Australian gain on sale is measured from that old, low figure, not from its value when you inherited it. The one relief is for an asset the deceased had owned since before 20 September 1985, where the cost is instead its market value at the date of death.
Two further points sharpen the trap. The main-residence exemption that shelters an Australian home from capital gains generally does not apply to a foreign property or where the deceased was a foreign resident, so you should assume the Indian property is fully within Australian capital gains tax on sale. And while you hold it, any Indian rent it earns is taxable to you in Australia, with a credit for the Indian tax deducted. None of this is a reason not to inherit, but it means the records matter enormously: the deceased's original purchase cost, the dates, and a valuation at the date of death. That is exactly what we preserve on the Indian side, alongside the legal heir paperwork, a certificate confirming no Indian inheritance tax is due, and repatriation of any inherited funds to you, so that when you do sell, years later, the Australian gain is computed correctly and not overstated.