Yes, a well-planned vegan diet is able to meet the nutrition requirements for both pregnancy and breastfeeding. As is the case generally, you don't need to eat heaps more while you're breastfeeding. There is only a small increase in the amount of food you need to eat during this time. So long as you are eating a wide variety of foods, with plenty of fresh fruits, vegetables, legumes, grains, nuts, seeds etc. (i.e. not relying on 'junk' vegan food), then you should be getting most of the vitamins and minerals you need.
In general, dietetic associations will recommend that you pay particular attention to ensuring you are getting enough calcium and zinc in your diet. Vegan foods high in calcium include tofu, almonds, sesame seeds, tahini, spinach, oranges, figs, black molasses, broccoli, kale, parsley, chickpeas and even wholemeal breads. Vegan foods high in zinc include nuts, seeds (e.g. pumpkin and sunflower seeds), whole grains, and pulses and lentils.
Of course, vitamin B12 is a vitamin that is essential for all vegans to supplement with, regardless of whether they are breastfeeding or not. Some vegans get enough in their soy milks and nutritional yeast use (granted they choose brands that are supplemented with vitamin B12), however others may not. Check how much you have in your dietary choices, and supplement if it is under 2.8 mcg (micrograms) per day.
Often people will tell you that you'll need to supplement with Vitamin D as well because some dairy products are supplemented with it. Vitamin D is created in your body through a reaction between your skin and ultraviolet light from the sun; hence really all you need to do is ensure you spend enough time outdoors each day. If you have white skin, this means usually exposing your face neck and arms to sunlight for about 15 minutes to half an hour each day, most days of the week (without sunscreen). If you have darker skin, you'll need to spend more time in the sun.
When you are getting your regular blood tests done with your doctor, you can ask him/her to conduct a vitamin B12 and D test to make sure you have enough of each, as your baby will be relying on you having enough in your milk for him/her - and the consequences of falling short can be devastating. To be honest, probably all women should be checking this, regardless of whether they're vegan or not, because contrary to popular belief: non-vegans can also be deficient!
Queensland Government, Healthy Eating for Vegan Pregnant and Breastfeeding Mothers (www.health.qld.gov.au/nutrition/r ...)
NHMRC Nutrient Reference Values: Vitamin B12 (www.nrv.gov.au/nutrients/vitamin% ...)
Office of Dietary Supplements, Vitamin B12 (ods.od.nih.gov/factsheets/vitamin ...)