Uhm buddy, you need to eat the eggs with the Oatmeal, matter of fact you need protein in every meal!
Besides Oatmeal is relatively low or moderate in carbs, I mean 1/2 cup is only 27g with 4g of fiber. I eat a Multi grain Oatmeal with Oats, Barley, Rye, and wheat. The barley helps your body keep a leveled blood sugar throughout the whole day so when you eat your last carb + Protein meal of the day, your body doesnt have a huge surge of Insulin.
A good Breakfast meal for a cut is 1 cup of Egg Beaters, 1 whole Egg, 3/4 cup of oatmeal, with 8 sliced strawbarries. maybe a half grapefruit too. Dont over do the fruit if you want optimal fat loss! Your breakfast is also suppose to be your largest meal of the day.