Heat a grill or grill pan to medium heat. Lightly brush one side of the pizza dough with half a tablespoon of olive oil. Place the dough oil side down, and grill until the bottom is nicely browned and firm to the touch, about 3 to 5 minutes. Brush the top side of the pizza dough with the remaining olive oil and flip over. Top the pizza with the shredded bbq chicken, the red onions and the mozzarella cheese. Close the lid and let cook until cheese has melted and chicken is heated through, another 2 to 3 minutes.