In a medium saucepan over high heat, bring quinoa and water to a boil. Reduce heat to medium-low and cover. Simmer for about 10 minutes or until the quinoa is tender.
Remove quinoa from heat and let stand, covered, for 5 minutes. Then fluff quinoa with a fork and spread it out onto a large, rimmed baking sheet to cool.
In a small bowl, whisk lemon juice, garlic and pepper. Whisk in oil little by little to make the dressing.
After the quinoa has cooled, put it in a large bowl. Add the dressing, cucumber, tomatoes, parsley and onion. Top with feta cheese and toss gently to mix.