Our liver stores glycogen, which it can convert to glucose and send to the blood stream in times of fasting, or when we exercise, are ill, or under stress. This is a natural occurrence that happens to everyone. This is termed a liver dump or dawn phenomenon. In the mornings our bodies are in a state of fasting so our livers try to protect us by dumping glucose to help us start the day. There are hundreds of threads about this if you do a search.
Your post meal readings are reasonable for a newly diagnosed person, (although 9.5 is a bit high) but it is your before meal readings that will show you what levels your body runs at normally. This is an important figure to know because your post meal readings mean nothing without knowing your before level. You need to know by how much you rise after eating. Too high a rise and carbohydrates in that meal caused it and need attention, either by eliminating that carbohydrate element or cutting down on the portion size.
Please have a good read round the forums and the main website. All the information is there. Ask as many questions as you like.