well the safe response is to say if she has high blood glucose (over 13 mmol/l) then she shouldn't exercise.. the reason behind this is that high blood glucose could indicate inadequate insulin present.. when exercising therefore the body has to break down fats for energy (as there is limited insulin to utilise carbohydrate / glucose) potentially further increasing levels of keytones (which are released when the fat breaks down).. combined with fluid loss during exercise this is a recipe for DKA (Diabetic Ketoacidosis), which is she hasn't experienced is certainly not something that I would wish on anyone!
Normally you would check for keytones before exercising if your blood glucose were this high, so unless she can check for keytones.. which normally means pee sticks! to be on the safe side she probably should not..
Injecting before exercise is a risky business.. in a healthy individual the body actually stops releasing insulin as exercise commences to ensure blood glucose doesn't drop to rapidly and dangerously.. now it can be ok to inject but you need to remember that the insulin is going to be faster acting due to increased heart rate and also the body is going to be burning glucose and therefore such a large dose is not required... Further post exercise her muscles will begin to replenish glucose stores and therefore blood glucose can drop for up to 6 - 8 hours.. unless she has a good understanding of how her body works I wouldn't recommend it.