You might. B12 these days mostly comes from animal products, but it's also found in some fortified foods like Nutritional Yeast and Vegan Yogurt. B12 is an important vitamin for your overall health so it's not good to be low on it.
Animal products are high in iron, but so are the heartier vegetables like spinach, beans and lentils so you might not need an iron supplement. D3 is made by our bodies when the sun hits our skin. If you wear a lot of sunscreen or don't go out much, you might need a D3 supplement.
The only way to know for sure is to go to your doctor and get your blood tested. Tell your doctor you're eating a plant based/vegan diet (listen to the lecture about why you're wrong) and ask if you need to do anything special to make up for not eating meat, dairy or eggs. Just remember that most general practitioners have ZERO training in nutrition. It's ok to question their advice or to get a second opinion from a doctor who is educated on the healthy, plant based way of eating (WOE).