Unfortunately Brisbane, or Australia as a whole, isn’t as good as most overseas for dog friendly places. Our health and safety rules are quite strict which means dogs can’t go to coffee shops/food places, hotels, most accommodation places, most beaches, unfenced parks etc and generally need to go to designated enclosed dog parks for off leash activities.
In saying that, some of the off leash areas are beautiful. Best thing is to always check online for parks and walks and where you can safely go. An example is Raby Bay dog park which is where the dogs can run on the beach and swim. In Cleveland, it’s a great place to go for a day out in a beautiful waterside environment and gateway to the islands, reached via ferry.
Closer to the city centre is the Powerhouse Park on the Brisbane River. Huge park covered by trees and picnic areas with an enclosed dog park. Very popular place for both dogs and humans within easy reach of Brisbane City itself.
We need to catch up with the rest of the world insofar as where our pets can go I’m afraid but Brisbane is small and extremely lush so walking a dog on lead is still a great experience. Off leash areas are plentiful and well maintained.