The phrase can be interpreted in several ways. One interpretation is that it refers to the sheer physical beauty of Australia, such as its pristine beaches, majestic mountains, and vast outback landscapes. Another interpretation is that it refers to the unique and diverse array of plant and animal life found in Australia, many of which are not found anywhere else in the world.
Overall, "of beauty rich and rare" is a phrase that celebrates Australia's unique and special natural heritage, and it evokes a sense of national pride and appreciation for the country's natural beauty.