I would hold off on the eggs until after the run, when your body could really use the protein boost for repair and rebuilding. It is usually a good idea to have something
in the tummy, but for a 30 minute run, 100 to 200 calories of simple and complex carbs should be enough to see you through.
Everyone is different, but I really do not like running on even a moderately full tummy. Sometimes coffee with a heaping teaspoon of honey is all I need. And then I use the eggs and toast as the incentive for running back home faster