So the Royal couple were delighted to see and handle a bilby downunder. Wiki:
Bilbies have the characteristic long bandicoot muzzle and very long ears. They are about 29–55 cm in length. Compared to bandicoots, they have a longer tail, bigger ears, and softer, silky fur. The size of their ears allows them to have better hearing as well.
They are nocturnal omnivores that do not need to drink water, as they get all the moisture they need from their food, which includes insects and their larvae, seeds, spiders, bulbs, fruit, fungi, and very small animals. Most food is found by digging or scratching in the soil, and using their very long tongues.
They’re suited to semi-desert areas.
The wombat is more widely spread. Wiki:
They are adaptable in habitat tolerance, and are found in forested, mountainous, and heathland areas of south-eastern Australia, including Tasmania, as well as an isolated patch of about 300 hectares (740 acres) in Epping Forest National Park in central Queensland.