The getaway that is closest is Yarra Valley. Here, amidst the fern glades, towering forests and villages, you'll come across native Australian birds and animals like Tasmanian Devils, platypus, lyrebirds, echidnas, koalas and more. Next on the list if short travel time is preferred is Mornington Peninsula. You can do some birdwatching at Ashcombe Maze & Lavender Gardens and then go to Moonlit Sanctuary and see some reptiles and endangered animals. A long and pleasant drive away is Great Ocean Road where you can enjoy Australia's diverse wildlife.
If you are considering flying, then you should fly to Canberra and among the well-preserved parks and reserves you can enjoy the native flora and fauna. You could also fly to Adelaide, which is a little further away compared to Canberra, and enjoy the native Australian wildlife in the many parks, gardens and zoos. A slightly longer flight will take you to Sydney. Here you can enjoy the native wildlife at the Royal Botanic Gardens.