"Veganism at 14?"
It's possible for veganism at fourteen. However before becoming a vegan, you really need to understand far more about nutrition, than what little is taught about it in school. While this question was originally in the Vegetarian and vegan section, and has been moved since the original place it was at, I'll still try to answer it. However my answer isn't going to be short either. I'll be giving some information aimed at helping you. Now I will qualify here, that i am NOT a vegan, or vegetarian, but I am reasonably knowledgeable about it.
However being a vegan should NOT affect your period, unless you drop below the critical weight, for it to start, and continue. However some MAY TRY to claim otherwise.
However done right, with the proper research into nutrition, you should develop normally. But jumping straight into a vegan diet, without doing the needed research, can result in very serious health issues. In becoming a vegan, you will need to become something of a self taught expert, on nutrition. Mainly some types of anemia, and predominantly in the vitamin B complex group. An iron based anemia though, is not nearly as big of an issue, as some make it out to be if you know what to eat, and in some cases what to do, to get the benefit from the vegetables that are good sources for it.
However in the vitamins the biggest concerns for vegans, are as stated before the vitamin B complex, and vitamin D specifically vitamin D3, along with possibly vitamin K2. A quick note though on vitamin the K group, a lot is still unknown about it, and the various sub-types. However it's believed to help Vitamin D with calcium in the bones.
The three main ones in the vitamin B complex that a deficit can easily result in are B6, B9, and B12, which can result in anemia. Vitamins B9, and B12 if the deficiency is to big can turn into megaloblastic anemia, and can result in hospitalization. Vegetarians, and more so vegans, are advised to at the least to take a vitamin B12 supplement. The only known source for vitamin B12 is through meat, and the animal products dairy and eggs. It's strongly recommended, for both vegetarians, and vegans specifically, to have blood work done for deficiencies, twice a year, mainly for vitamin B12. However even those of us who eat meat, along with dairy and eggs, can be deficient in vitamin B12. In the U.S. at least fourty percent of all the population is deficient in vitamin B12.
The next big one is vitamin D, although called the sunshine vitamin, without meat, there are only two known sources for it. The two sources are lichen, and the other certain types of mushrooms but only after being irradiated with light, from the ultraviolet blue frequency range. However a vitamin D deficiency, even with fortified foods, is one of, if not the largest deficiency in the U.S. at an estimated eighty to ninety percent of the overall population. So it's strongly suggested to be checked for a deficiency in vitamin D as well. There is a vegan compatible of vitamin D available in the form of D2. However the conversion rate from D2, to D3 may not be that good. Vitamin D is also very important to bone health due to its role, in helping transport calcium to the bones.
Now there's another issue, and that's the omega fatty acids, specifically the omega three fatty acids. Vegetarians, and vegans need a good source of them, to maintain the proper balance, although even those of us who eat meat also tend top have an imbalance due to our diets. The omega six fatty acids, tend to be out of the proper ratio at sixteen or greater omega six fatty acids, to one omega three fatty acids.The proper range should be between four omega six fatty acids to one omega three, to one omega six fatty acids, to four omega three fatty acids.
The biggest fallacies about the vegetarian/vegan diet is a lack of protein/amino acids, calcium, and iron. These are easily found in plant matter, and with protein, knowing what foods compliment one another to make the proper protein chains. Now in doing the research, that I mentioned earlier, you will need to learn the best sources for proper nutrition. One place to start is researching the various basic foods, and what they have. Below is a simple easy to use search.
broccoli cooked nutritional value
Here's one result from that example.
http://nutritiondata.self.com/facts/vegetables-and-vegetable-products/2357/2
In the above example you can adjust the serving size weight, to one ounce, or one hundred grams, for side by side comparisons of different foods, with the drop down. I use nutritiondata.self.com frequently due it giving the most complete breakdown, across the board, on all nutrients. While it lacks in some places, for now it's the best I've found.
Here are two other links to help start learning about the various elements of nutrition. Although I'm not overly fond of Wikipedia, it can give a good start in the basics.
https://en.wikipedia.org/wiki/Essential_nutrient
https://en.wikipedia.org/wiki/List_of_macronutrients
In sources I will add three more links, for you to read through.