In terms of post-running nutrition, there are a lot of thoughts surrounding this - but there is one major theme, ensuring that you have carbohydrates to replace the energy you have used (refuelling), and protein for muscle repair (I can see that you already have eggs, and milk, which is good!). In terms of recovery, it is often touted that a 4:1 (or sometimes 3:1) carb:protein ratio is optimal, and that the protein should be consumed within an hour of finishing the run (as this is the time that it will have the most effect) - however, the body can only make use of so much protein per hour (based on your body weight), and different sources of protein act over different timescales (milk protein, for example, acts over a longer timescale than whey protein). Resources on websites such as RunnersWorld cover these topics.
So, having established the composition of what you should be eating - it's a case of working out a good way of having a wholesome breakfast that incorporates this!
As you run before breakfast, which naturally means your body is depleted, you must definitely ensure that you have carbs (porridge, etc) otherwise you may feel sluggish towards lunchtime as you increase your distance.
Here is a nutrition section from RunnersWorld,
Here is an article for joint-health
Here is an article outlining the timings for protein intake
As you are just starting out running, these sorts of articles will help you on your way - I hope this helps, and all the best!