Also not a doc, and I agree with ES.
Ketones sometimes show up in urine after exercise (even for non-diabetics) because of burning some fat due to unavailable carbos. Exercise is so very important for good diabetes management, and it's wonderful when a child who has diabetes finds a sport or two that s/he loves participating in. It'd be important to discuss the patterns of blood sugars and patterns of ketones with the child's endocrinologist/ diabetologist.
I'm not a doctor, so I would definitely run that question by a physician just to be sure. However, as a diabetic myself, I have never found exercise to be harmful. The usual precautions should be taken - warming up, checking blood sugars before and after exercise and keeping snacks handy in the event of a low blood sugar. It is possible to have occasional ketones in the urine and to feel fine the next day. If ketones are there for an extended period of time, that could present some more serious concerns. But in that case, you probably wouldn't feel well enough to run or exercise anyway.
I'm a big believer in listening to your body and if you feel good enough to exercise or whatever, you should go for it, as long as it is a healthy, reasonable activity and backed up by the usual equipment - blood monitors and snacks. Have fun and go for the goal!
Es