I spent some time in Papua New Guinea and found it easy to eat there..Yams are readily available as is rice. Fresh fish was also available. Tropical fruits were available at all meals and I would buy some to have them with me for snacks. I do think it is important to take some crackers and bars to have as a back up and I also had a letter from a physician stating it was necessary to carry food just incase getting through customs became an issue.
Brisbane Australia had SIGNS outside the restaurants saying we serve gluten free food. That was such a treat to see.