achtungbaby,
The answer is that for the 12" pizza you would use 44.44% of the ingredients for the 18" pizza. Where does the 44.44% come from? It is the ratio of the squares of the radii of the two pizzas, or 36/81 = 0.444444, or 44.44%. To prove out the math, compare the two hypothetical formulations below that are identical but for the pizza sizes:
Dough Formulation for 18" PizzaFlour (100%): Water (62%): IDY (0.45%): Salt (1.75%): Olive Oil (1%): Sugar (1%): Total (166.2%):
 426.43 g  15.04 oz  0.94 lbs 264.39 g  9.33 oz  0.58 lbs 1.92 g  0.07 oz  0 lbs  0.64 tsp  0.21 tbsp 7.46 g  0.26 oz  0.02 lbs  1.34 tsp  0.45 tbsp 4.26 g  0.15 oz  0.01 lbs  0.95 tsp  0.32 tbsp 4.26 g  0.15 oz  0.01 lbs  1.07 tsp  0.36 tbsp 708.72 g  25 oz  1.56 lbs  TF = 0.09824

Dough Formulation for 12" PizzaFlour (100%): Water (62%): IDY (0.45%): Salt (1.75%): Olive Oil (1%): Sugar (1%): Total (166.2%):
 189.52 g  6.69 oz  0.42 lbs 117.5 g  4.14 oz  0.26 lbs 0.85 g  0.03 oz  0 lbs  0.28 tsp  0.09 tbsp 3.32 g  0.12 oz  0.01 lbs  0.59 tsp  0.2 tbsp 1.9 g  0.07 oz  0 lbs  0.42 tsp  0.14 tbsp 1.9 g  0.07 oz  0 lbs  0.48 tsp  0.16 tbsp 314.99 g  11.11 oz  0.69 lbs  TF = 0.09824

Note the final dough ball weights: 25 ounces for the 18" pizza and 11.11 ounces for the 12" pizza. The ratio of 11.22/25 = 0.4444, or 44.44%. The same ratio applies to all of the individual ingredients. Also, the physical characteristics will be essentially identical. You can also use the same percent for sauce, cheese and toppings. However, you will need to know how much sauce, cheese and toppings are used by the 18" pizza. In the above example, you would multiply those amounts by 44.44%.
As I was composing this reply, I see that parallei was posting. He got the correct answer. However, you can leave out pi (3.14159) in calculating the areas since they cancel out. You only need to use the ratios of the squares of the radii.
Peter