Yes, it's quite normal and natural - your body needs energy to get going in the mornings, and if you haven't eaten for a while (i.e. overnight) then your liver will usually offer a helping hand in the form of a liver dump and you get a rise in glucose levels. And this dump happens to diabetic and non diabetics alike.
When you've been low (enough) carbing for a while your body should learn to switch over to burning fat as needs be, and since it can also store much more of this than it can fuel from carbs, your liver will have less work to do, and so you should hopefully see a reduction in your morning levels.
Robbity