Preheat oven to 350 degrees F (175 degrees C). Line a baking sheet with parchment paper.
Beat butter, brown sugar, and white sugar together in a bowl until fluffy. Add egg and vanilla extract; mix until combined.
Whisk flour, baking soda, and salt together in a bowl; add to butter mixture until dough is just mixed. Fold in oats and quinoa. Drop dough by teaspoonfuls onto baking sheet, approximately 2 inches apart.
Bake in the preheated oven until edges are golden, 10 to 15 minutes. Let cool on baking sheet for 5 minutes; transfer to a wire rack to cool completely.