DP is a pain Juliette. It occurs because everyone's liver decides that a few hours prior to waking up you'll need some glucose is your bloodstream to give you energy for the coming day. In non diabetics it's not an issue because an insulin response quickly mops up the excess. In diabetics with either weakened or resisted insulin responses the raised level can hang around for hours. There is little you can do although low carbing seems to gradually reduce the amount of DP you experience over weeks and months. What I have found is actually producing a small safe but definite spike with breakfast kicks my systems into action and will reduce the DP level quicker than either having no breakfast or a very low carb one that would produce very little insulin response. I will specifically eat around 25g of fruit (strawberries, raspberries, blueberries etc.) with some plain Greek yoghurt so that the sugar in the berries will provide the "kick start".
You can also do a brisk 5 or 10 minute walk after breakfast as I've found that helps too. Nowadays my BG's are largely in the 4's from late morning onwards but can still reach high 5's first thing on many days because of DP.
Wouldn't worry about it too much though.