Tiredness and diabetes may not be very strongly connected. While rapidly changing sugar levels may introduce additional strain on your body, pregnancy puts even more stress on it on its own.
In general, women often feel very tired and weak during the first trimester. My wife slept around 11 hours, lay a lot during the day and felt constantly tired even without diabetes. I have a friend who, from what she says, feels even worse. Combine all this with morning sickness, hormones, and the psychological stress (OMG I'm going to have a baby;) - and you'll get te picture. All of this is completely normal.
Gestational Diabetes has to be properly managed, otherwise it may cause undesirable effects on mother and the child.
Fortunately, a proper diet and some exercise is often enough. The daily amount of calories has to be set based on mother's BMI. The diet must consist of as little simple carbohydrates as possible, to avoid rapid spikes of blood sugar. Especially breakfasts must be chosen properly, because insulin resistance is highest in the morning.
Moderately intense physical exercise often helps to manage GD. Personally, I'd suggest aerobics (though remember, that not all exercises are good for pregnant women!) - it keeps your heart rate reasonably high and does not introduce heavy stress on your body.
As always, it is very important to follow your doctors suggestions and consult him whenever you are in doubt. All advice you can find in the Internet, including mine, may be wrong or just not applicable to your specific case.