You can bodysurf in Far North Queensland!

Clifton Beach 24 km north of Cairns

Kewarra Beach, 20 km north of Cairns

Far North Queensland beaches usually have little or no waves (there's a big bloody Barrier Reef out there). But around June/July you get some nice waves on the Northern Beaches (Palm Cove, Clifton Beach, Kewarra Beach). No one is in the water, even though it's warm (around 26 degrees C). Why loll around a resort pool, listening to screaming kids?
Ignore the beach signs, the locals do. Stinger (e.g. Box Jellyfish) Season is roughly October to May. Stay clear of waterways near the mangroves (saltwater crocs).
It's so easy to get from Cairns to the Northern Beaches. The public Cairns bus (Translink) costs $5.50 one way. Comfortable, reliable and half-hour service during weekdays.

This sign greets you at the beach entrance (Pullman Sea Temple, Palm Cove, 26 km from Cairns)