The state Senate’s new power-sharing duo stepped out as a couple for the first time in public yesterday, appearing in the Rockaways to announce a Senate Hurricane Sandy recovery task force.

Republican leader Dean Skelos and Independent Democratic Conference chief Jeff Klein of The Bronx said their unprecedented coalition to run the Senate is a go.

“Senator Klein and myself personally have looked each other in the eye and said, ‘We’re going to make this work; we’re going to show that this new model of government can work,’ ” said Skelos, of Nassau County. “It’s going to happen.”

Klein’s five-member group of breakaway Democrats and Skelos’ GOP conference agreed to unite under the two men’s leadership after Republicans fell to 30 members in the 63-seat Senate in the last election.