Preheat your oven to 350°F (175°C).
In a medium bowl, whisk together the gluten-free all-purpose flour, baking powder, baking soda, and salt. Set aside.
In a large bowl, cream together the softened unsalted butter, granulated sugar, and brown sugar until light and fluffy, about 3-4 minutes.
Add the eggs and vanilla extract to the butter and sugar mixture, beating in the eggs one at a time. Gradually add the dry ingredients to the wet mixture and mix until just combined.
Gently fold in the rainbow sprinkles until evenly distributed throughout the dough.
Using a cookie scoop or tablespoon, drop rounded balls of dough onto prepared baking sheets, spacing them about 2 inches apart.
Bake in the preheated oven for 10-12 minutes, until the edges are lightly golden and the centers remain soft.
Remove from the oven and let cool on the baking sheets for about 5 minutes before transferring to a wire rack to cool completely.