You are likely to feel healthier on a vegan diet, provided you eat properly.
The major areas to watch are:
Calcium – plenty of fresh greens and vegetables like broccoli and spinach. You can also buy soy milk, orange juice and breakfast cereals that are fortified with calcium as well as vitamin D.
Iron – beans, greens, dried fruit, molasses and nuts.
Adequate amounts of Vitamin D are obtained fairly easily from limited, sensible exposure to gentle sunlight. It is also available in fortified orange juice, soy milk and breakfast cereals.
Vitamin B12 is hard (though not impossible) to get from a vegan diet, but there are also specific B12 supplements that might be a better way of getting that particular vitamin. A B12 dot or drop that dissolves under the tongue is the most reliable source.
Eat a good variety of foods, of all different colours. Generally, the deeper the colour, the better the fruit or vegetable is for you. Most of your diet should consist of fresh, whole foods like fruits and vegetables (preferably raw, as in salads), whole grains like brown rice, and beans and legumes. Nuts and seeds are a good source of protein as well as other nutrients.
Don’t worry too much about protein – it is quite difficult to develop protein deficiency. The average eater could benefit from eating less protein, and certainly replacing some of the animal protein with plant protein is beneficial in many ways. Protein is present in all foods (in varying amounts), but good sources for vegans are beans, tofu, (certain) whole grains, nuts and seeds.