Hi Mun,
It sounds like classic dawn phenomenon results. During the early morning your body releases glycogen from the liver to prepare the body for action. Good for a non-diabetic, disastrous for a diabetic! The only way I've found to sort this out properly was to have an extra injection at 0630 when I first woke up so that my BG didn't sky rocket before I had breakfast an hour later. However, going onto pump therapy has saved me from this hassle as I just have more basal between 0630 and 0900. It's definitely worth taking your results to your doctor/consultant and discussing them as they may have alternative strategies for you.
xx