Preheat oven to 350 degrees F (175 degrees C). Place acorn squash cut-side down in a baking pan.
Bake acorn squash in the preheated oven until tender when pierced with a fork, 30 to 40 minutes. Flip to face up and cool until easily handled.
Bring water and quinoa to a boil in a saucepan. Reduce heat to medium-low and simmer, covered, for 10 minutes. Stir in prunes, raisins, apricots, garlic, and ginger. Cook until prunes, raisins, and apricots plump up and quinoa is tender, about 5 minutes.
Drizzle olive oil over quinoa mixture and add salt; mix well.
Scoop flesh of the acorn squash from the shells; cut into cubes and toss gently with quinoa mixture. Stuff empty shells with mixture. Sprinkle pecans on top.