I don't feel that it is good to workout unless you have taken at LEAST 2 Good meals with plenty of carbs prior to workout. If you absolutely must, I would wait about 2 hrs.
you could probably do it an hour later- one and half hours, however, you'll probably run out of energy pretty quick, if you're going with a intense workout. If you're just talking about cardio, then its a different story.
Try only eating 1-2 granola bars or eat a banana and drink a glass of milk. Your stomach should feel full enough to get you through the workout without getting sick. Then eat your breakfast after your workout.
If you wanna throw up it could also mean that you are training with the right intensity - which i like...A lot.
If morning training is the only opportunity you get then it will have to do. The amount of carbs you have had to saturate your glycogen stores in your muscles will obviously be minimal so this could affect your progression. You could always take an energy drink in with you and drink it between sets while you train. [perferably a 'still' or 'flat' i.e. non-fizzy drink so it doesn't upset your stomache as you train.]
wake up about 3 and a half hours before you train...... eat and go back to sleep....... wake up and eat 50 grams of carbs before you go... about 20 minutes before you start........ hey it could work........ since you dont have time to wait 2 hours this may do the trick