Esom Ioka scored a rapid hat-trick against New Zealand last week, but the Cook Islands have lost to both the Kiwis and Fiji.
Australia forward Cameron Murray was ruled out of Saturday night's World Cup match in Townsville on the day of kick-off.
News Corp reported that David Fifita would take Murray's place on Kevin Walters' six-man bench.
Murray completed Friday's captain's run before developing general soreness, and a mild illness had also left him below full fitness.
Walters rested him for the Kangaroos' third match of the campaign.
Murray recorded a category-two result in a HIA last week, but is believed likely to be available for Australia's semifinal next week.
The Kangaroos remain unbeaten after beating Fiji, although they have yet to produce their best football.
Walters said the team could continue improving as it seeks to defend its World Cup title.
"We're still yet to find the best form, so that's exciting for me and the rest of the team," he told Courier Mail.