random.js

Object.prototype.random = function() {
  return this.toRandomArray()[0];
};

Object.prototype.toRandomArray = function() {
  function object_values(object, values) {
    Object.keys(object).forEach(function (key) {
      typeof object[key] === 'object'
        ? object_values(object[key], values)
        : values.push(object[key]);
    });
    return values;
  }

  return object_values(this, []).sort(function() {
    return 0.5 - Math.random();
  }); 
};

var obj = {
  a: 1,
  b: {
    x: 2,
    y: 3
  },
  c: {
    z: {
      q: 4
    }
  }
};

console.log(obj.toRandomArray());
console.log(obj.random());