At age fourteen your body requires quite a bit of protein, because you are beginning your growth spurt. the recommendations for limiting protein you will read on most sites are intended for adults who have finished growing, so ignore them. Not only that, but your brain will be growing and developing for at least the next ten years, so you need large quantities of saturated and monounsaturated fat to fuel that growth. The brain is mostly made of fatty acids and cholesterol. Although plant sterols are not useful to the human body, you do not need to eat animal foods to get enough cholesterol, so long as you eat enough saturated and monounsaturated fats.
I would strongly advise you, however, to postpone embarking on a vegetarian diet until you have attained your adult stature and your brain has stopped growing. Vegetarain keto can be done, but keto is a lot easier to do when animal foods are an option. Your health is precious, and you can permanently damage yourself by failing to eat a healthy diet during puberty. The key to a ketogenic diet is to eat as little carbohydrate as possible, and that is very difficult on a plant-based diet.