Hi Kathy, I am from Australia.
I haven't been up to Cooper Pedy yet although I know people who have and thoroughly enjoyed it. Years ago I've been gold fossicking out at Hill End though didn't find too much gold.
Do you enjoy going through caves? The Wombeyan Caves (south of Sydney) or Jenolan Caves (west of the Blue Mountains - lots of hiking trails there) might appeal to you and have lots of interesting rock formations although none you can take for souvenirs!
Further north from Cairns is the Daintree rainforest - you can do cruise tours there.
It is a lot of driving - it all depends how long you have and how much driving you like, but to drive Sydney to Cairns would take approximately three full (ten hours) days driving.
As you are coming in an off season I don't think you'd have much trouble getting accommodation especially during the week.
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