The Douglas Shire has electric BBQ's in Port Douglas, Cooya Beach, Mossman, Newell Beach, Wonga Beach and Daintree Village.

There are 2 BBQ's between the beach end of Macrossan Street and the surf club:

At the southern end of Fourmile Beach where Barrier Street reaches the park between the Beach Shack and the Barrier Reef Tavern:

Some of the best things in life are free.
Depending on when council clean the BBQ's you may need some sort of scourer to clean the cooking surface first or use cooking foil. The cleaning schedule is week days mid to late mornings and council does a great job.
More detail on Daintree BBQ's