First, novice runners, and even many verterans, react differently to eating before a run. My first suggestion would be to use the Galloway run/walk method. Look it up online. Your walk break and run periods might be too long. Cut the walk time down to 1 minute or 100 meters (1 quarter of a lap). Cut the run time down until you can recover enough in one minute (100 meters) to do it again. At first, you might run only 30 seconds. If that's the case, you would run 30 seconds, walk 60 seconds, and repeat until you covered your desired distance. Gradually over the next few weeks, you can increase the run time to 45, 60, 90, and 120 seconds. However, the walk time should remain at 60 seconds for the next few months. In my experience, when you walk longer than 60 seconds, it's harder to start running again.
As far as eating is concerned, everyone is different. Until you figure out what works for you, I suggest that for right now (not for forever), you eat only enough to boost your morning blood sugar and be quickly converted to energy. That might be one piece of dry toast or a fruit cereal bar. These quick acting carbs will boost your blood sugar in about five minutes. If you can't handle solid foods, you could try coffee with a creamer that includes sugar, or you might try apple juice, grape juice, etc.
Your muscles have enough stored energy to run for an hour or more without a morning meal, but it takes a few minutes of running for your blood sugar to get up to the level you need. Your morning carbs are a way to elevate your blood sugar so it's high enough when you first start running. (Okay, that might not be completely accurate in how the body works, but it covers the gist of what's happening to you.) Try it and see how it goes.
Again, everyone is different. I absolutely cannot eat even one egg (70 calories) within two hours of running, but I can handle a 100 calorie fruit bar, even if I eat it just prior to doing my warm up drills. You need to experiment and see what works for you.