COHUNA, Australia—The world’s driest inhabited continent is struggling to sustain its pioneering effort to put water supply in the hands of market forces, as authorities contend with a drought and complaints by farmers who say the system is putting them out of business.

Australia has one of the world’s most sophisticated water-trading systems, and officials in other water-challenged places—notably California and China—are drawing on its experience to manage what the World Bank has called world’s “most precious resource.”