Bake it on a lower heat, maybe 130 fan and if it looks like it's going a bit too dark too quickly around the sides puts some parchment on the top and around the edges after 2 thirds of the baking time. Hope it goes well!
Bit late for you, but you can convert any recipe by working out the volume difference (what you are doing with water, but with maths.;)) So you have a recipe that makes an 8" round cake and uses 4 eggs, say. Assume your cake is 3" deep when baked. Volume of a cylinder is pi (3.14) x radius x radius x depth. So 3.14 x 4 x 4 x 3 = 150.72 The volume you want is 12 x 9 x 3 (to get a 3" deep cake) = 324. You can see already it's roughly double, but if you divide one by the other you get 2.14. If you multiply that by your eggs you get 8.6 - just round it up to 9. I know it seems like a faff, but once you know how to do it you can convert any size to any other size and shape.