In a medium bowl, combine the coconut milk and chopped dates. Using an immersion blender, blend until the dates are completely smooth and incorporated into the coconut milk.
Add the quinoa to a medium pot over medium heat to toast. Stir constantly for about 10 minutes, until the quinoa starts popping, turns golden, and becomes fragrant.
Carefully pour the coconut-date mixture, almond milk, salt, and vanilla extract into the pot with the toasted quinoa (take care, as it may splatter). Place over medium heat and bring the mixture to a boil, stirring frequently.
Reduce the heat to a gentle simmer. Cook for about 35 minutes, stirring often, until the pudding thickens and the quinoa becomes soft and translucent.
Divide the warm pudding evenly among 6 single-serve jars, or transfer it to an airtight container. Serve warm or chilled. Store covered in the refrigerator for up to 4 days.