Mariela,
I'm not Cathe either, but I am an exercise physiologist. Exercising first thing in the morning without eating at least a little something is a bad idea. Here's why.
After a night of no food, your body's glucose/glycogen stores are depleted. Because of the way your body breaks down fat to fuel exercise and because glucose is a necessary fuel for both aerobic and anaerobic metabolism, you have to replenish your supply before asking your body to work--that is, unless you want to compromise lean muscle tissue.
The idea that you have to deplete glucose/glycogen stores before you burn fat is a big myth. Both fat and glucose are being burned at all times in varying amounts. In truth, if blood glucose and glycogen stores are depleted, fat can't be metabolized at all as a fuel for exercise. What will happen is the body will then have to make glucose from other substances. While a little fat is used in this process, protein is used to a much greater degree, so the result is a greater loss of lean tissue than fat tissue.
Also, when the body has to make its own glucose from other sources, it doesn't keep up with the fuel demands of exercise. You poop out and won't be able to exercise nearly as intensely, especially with your strength training.
The moral of the story is to stoke your engine before you ask it to work--eat breakfast, even if it is only a piece of toast and a glass of juice, or a banana. Just don't go for it without refueling!
Maribeth