Batteries should be about 50% charged & carry on as hand/cabin luggage, on all the airlines, I believe.
If you want to fly on the strand you will need a CASA clearance as you'll be within 5 km of the airport.
I live in Tsv. never had a problem but then I know some of the areas. i.e. The boat ramp at South Townsville. At the end of the road by the Entertainment centre & casino. Magnetic Island. Paluma water falls north of Tsv. Go to the "I" center to find out the places of interest would be my suggestion.