When baking a large, single layer carrot cake the temperature should be relatively low, but if the top of the cake begins to darken alarmingly, do cover it with foil during the last 20-30 minutes ...
Recipes for larger layer cakes mix and bake one layer at a time, so you can mix a manageable amount of batter and re-use a single large tin. The recipe uses UK medium eggs (approx 60g/2¼oz).