It's always best to check in the morning and two hours after each meal to get the best handle on how your blood sugar levels are running.
Having said that, the dawn phenomenon is one of the more puzzling aspects of diabetes, but also one of the easier ones to fix -- usually. A snack before bed helps, but it needs to be a specific kind of snack: a protein based one. Peanut butter on crackers, a piece of cheese, a piece of lean meat or a handful of nuts are all great choices. What this does is it gives the liver something to do besides dump glucose, since it is working to help metabolize the protein.
A diabetic with high fasting readings can always try the late snack first, since it won't run the glucose up, and check the results for several days, to see if he or she is experiencing DP.