There's a few nice dog friendly swimming holes about half hour from my house along one creek/river. I might spend some time playing Tarzan off the rope swing there while the dog can just chill out in the shallows. He doesn't like to go any deeper than where he can lay in the water. But there's days when it has too many people for my liking there. Anywhere more than zero and I have to evaluate if I'll stay.
There's a great walking track if I park on the opposite side of the road with three nice shallow swimming holes I can pick from. About 20 minutes from there is a place where every few years, a group rebuilds this medieval village. I've never showed up there when they've lived there for a week in as close to the conditions of the time as possible. But it's an interesting walk and fun to envision how I'd build my hut if I was involved. Probably another paddle on the way back. So that's my plan. Might even take a small portable cooker and cook up a bit of lunch/afternoon feed by the creek or in the village.
I'm not in Sydney though. I don't expect the temperature to feel as bad as we don't get the humidity here. But hopefully there's no sign of storms or the dog will opt out.
But everyone working outdoors, stay safe and hydrated. Heat stroke can be fatal.