I have Type 1 which I treat with insulin and have a primarily vegetarian diet.
There is myth that it is "too hard" to eat a low carb diet without meat but there are many meat alternatives without carbs such as quorn and tofu and seitan and, if you are not vegan, cheese and eggs.
There are many reason to chose a vegetarian diet but, as long as you eat a similar amount of carbs, managing diabetes is not the one.
If you feel good (physically, morally, ethically, ... whatever) eating a vegetarian diet, don't let diabetes be the reason to stop you. But, there again, if you are not vegetarian already, diabetes is not the reason to choose it.
As
@JoKalsbeek mentioned, any change in diet when you are taking insulin, means you will need to consider your insulin dose. This is easier if you count your carbs and maintain a similar level.
Bear in mind, hypos don't always come in "fast and hard"- they can also creep up on you. As you are taking insulin, I am sure you know this already.