Mare, I always exercise before I eat breakfast! I hit the gym every morning at 5:45 am for an hour on an empty stomach and I really don't think I'm burning muscle. My rule is no food till I exercise and since I love to eat, I'm there!!
Some trainers recommend cardio before eating for maximun fat loss but there really haven't been any good studies to back that idea up.
When you exercise, your body isn't burning off what is or isn't in your stomach anyway since that isn't even digested. Our goal is burning stored calories in the form of F-A-T, right? Exercise - along with calorie restriction - creates the calorie deficit that utilizes stored fat for energy.
So it's really a personal decision whether to eat or not before you exercise in the morning. Some people feel weak without a little snack, even first thing in the AM; others are like me and get queasy if they eat and then do maniacal cardio. If what you're doing is working for you, there's no reason to change.