Yes. It is a known issue with Diabetic 1's. The sunrise effect or the dawn phenomenon is a natural increase in blood sugar levels that occurs in the early morning, usually between 3 AM and 8 AM.
It's caused by a rise in hormones, such as growth hormone and cortisol, that signals the liver to produce more glucose for energy.

Yes my bg goes up as soon as I start moving around in the morning.

yes this happens to me