Put quinoa in a mesh strainer and rinse thoroughly to remove a bitter taste. Put in a 1-1/2-quart saucepan together with water. Bring to boiling and simmer, covered, about 15-20 minutes or until liquid is absorbed and quinoa is cooked.
Transfer quinoa to a medium bowl, let cool to a room temperature. Add tomato, radishes, corn, pickled cucumbers and onion; stir to combine.
In a small bowl, whisk together olive oil, lemon juice, pepper and salt. Add to quinoa mixture together with avocados; toss to coat.