I don't think it is so much the calories, as your body may not be producing sufficient ketones yet to support the need for fuel for the muscles. This puts you at risk of breaking down lean muscle mass to produce that needed glucose, as the body finds it faster to convert muscle to bio-available glucose/glycogen than it does for the liver to metabolise fat into ketones.
I certainly wouldn't recommend anything beyond walking or light yoga/pilates stretching in the first 5-6 weeks of P1, while your body is adjusting to ketosis and the change of balance from carb fueled to fat fueled.
However, longer term you need to assess how you feel. Gradually increase your exercise, but be aware of how your body is reacting to the level of exertion and pay a lot of attention to pre-fueling and post-fueling.
I walk 3 miles a day, strength train at the gym twice a week and have just started doing running intervals (albeit slow) in the walking. It CAN be done, but you need to look very closely at how your body is reacting and keep on top of tracking changes to body fat and weight on a daily basis, to know if you are burning fat or muscle.
Lots of people prefer to play it safe and restrict exercise, but many of us already have exercise routines and simply need to rethink how we manage them on a different fueling system and reduced metabolic rate.
Choose your vegetables carefully. I tend to look for higher carb/higher fiber and go for more protein dense meats and eggs over fish and tofu.
You may find more information on the bodybuilding and athletics sites on how people manage nutritional ketosis and their fitness program (albeit they tend to be higher fat ratios than IP uses).
As always, listen to your body. If you are already an athlete then you will be more familiar with the signs of fatigue and overdoing it.