I'm with Willyroo. I'd recommend a taxi into town, breakfast on the Esplanade at one of the numerous choices and a swim and doze under the palm trees at the lagoon. There are change rooms there to shower in. Allowing for the time the formalities at either end of the layover will take you'll have up to 4 hours.

I don't normally transit though Cairns but won't the OP re-check the bags just after exiting the customs hall?

Now if it's raining....