If you are traveling on most popular tourist route in Australia from Sydney to Cairns then you have good possibility to spot platypus in Eungella National Park. Park is located about North West of Mackay. It is about 80km from highway No 1. So it is only short detour from main route. Best time to spot platypus is before sunset or after sunrise. I was there just after sunrise and watched for an hour at least three platypus swimming around lookout platform or from the bridge.
Another place apparently is Carnarvon Gorge section of Carnarvon National Park, but can’t confirm it and this park is further away from highway No 1, but has good walking trails so worth a visit anyway.