In the bowl of a stand mixer or a large mixing bowl with a hand mixer, beat the butter for 1 minute on high until smooth. Add the sugar and cream for 2-3 minutes or until pale in color. Add the extracts and egg, and mix until combined, about 1 minute.
In a medium mixing bowl, whisk together the flour, oats, baking powder, and salt. Add to the wet ingredients, then mix until combined.
Wrap the dough in plastic wrap and chill for at least 2 hours, preferably overnight. Remove the dough from the plastic wrap and place it on a long piece of parchment paper. Place a similar-sized sheet over the top, then using a rolling pin, roll into a flat, even layer, about 1/4-inch in thickness. If the dough is soft and sticky, transfer it to the freezer for 15-20 minutes.
Preheat the oven to 350 degrees Fahrenheit (177 degrees Celsius). Line baking sheets with parchment paper or silicone baking mats, and set aside.
Working quickly, carefully cut out mini animals using animal cookie cutters and place them on the prepared baking sheets about 1/2-inch apart.
Place in the oven and bake for 10-12 minutes or until the centers are no longer soft and the edges are pale brown in color. Remove from the oven and allow to cool on the pan for 3 minutes before transferring to a wire rack to cool completely.
Meanwhile, in a medium microwave-safe mixing bowl, add white chocolate wafers and coconut oil. Heat for 30 seconds on half power, stir, then repeat twice more if needed. Whisk in the vanilla extract until smooth.
Turn each animal cookie upside down and dip it in the white chocolate. Swirl to remove excess. Add rainbow sprinkles, then return to the cookie sheet or additional parchment/wax paper to set. Cookies should be set within 20 minutes (refrigerating them will speed up the process). Cookies stay good at room temperature for up to 4 days. They aren't super fragile, which means they're perfect for lunch boxes!