The power of habit is extraordinary. If you have been used to driving, riding, or walking on the right side, your brain will need time to adjust to Australian streets, bike lanes and pedestrian platforms. In Australia, just like The UK, driving is happening on left side.
When you travel around the city, I would suggest using the public transport, just to stay safe. Car accidents have been reported when tourists drivers (especially Americans) hadn’t been prudent enough when switching from their normal to the ‘abnormal’ left side. If you really need to drive around Australia, then take it easy, slowly-slowly towards the destination, stop as often as you need to, just to allow yourself to get used to the change.
It has taken me more than three months to adjust and confidently ride my bike in Melbourne. But, hey, I am that type who needs to think which one is right and which left before turning. You are probably better than that!