I would argue that going vegetarian doesn't mean you won't get injured. it has nothing to do with it. If anything, you must supplement the diet so that you are ingesting enough protein to heal the delicate muscle fibers that get torn every day by the sheer force of hiking day in and day out. And I have seen more than one hiker start as veggies and eat a burger in the town after a few months.
There is no way to really avoid injury. The fact of the matter is, it WILL happen. It just matters how severe the innjury is and if you are eating well enough and doing what must be done on the trail to heal it
But to avoid overuse injuries, esp at the onset, start slow, carry less and use common sense. its not a race