In a large skillet, heat 1 tablespoon oil over medium-high heat; stir-fry shrimp until they turn pink, 2-3 minutes. Remove from pan.
In same pan, heat remaining oil over medium-high heat. Add ginger and garlic; cook just until fragrant, about 10 seconds. Add pepper, carrot and onion; stir-fry 2 minutes. Stir in pineapple and shrimp. Add rice and soy sauce; heat through over medium heat, tossing to combine and break up any clumps of rice. Stir in green onions. Sprinkle with peanuts; serve with lime wedges.