You could also post a picture of the grill and we could help identify it.
Really not many Q models out there. The older ones are 100s, 200s, 300s. Newer ones are 1000s, 2000s, 3000s. The 1s being the smaller and 3s being the largest.
The second number usually indicates if a lid thermometer came installed on the lid from the factory; ex: 220 or a 2200