Things you should be looking out for when you change to a dairy-free diet are two essential nutrients that can be lost when you change to a plant based and whole grain diet and no, calcium isn't one of them (that's found in plenty of plant based and whole grain foods), they're B-12 and Vitamin D.
B-12 is found only in animal products and fortified foods/drinks but is essential for forming red blood vessels and key in the normal functioning of the brain and nervous system. Vitamin D is either absorbed through the skin via direct sunlight or ingested through animal products or fortified food and drinks and regulates calcium and phosphorus absorption, maintains healthy bones and teeth and works with our immune systems.
If you have swapped milk for a dairy free substitute then have a look and see if it has been fortified with either B-12 or vitamin D, or both! Check your bread and other packaged snacks and substitutes (nutritional yeast, a vegan's best friend, is usually fortified with all the B vitamins, but check just in case). Chances are you'll be consuming enough. If you're making your own milk and substitutes from nuts and seeds then you could think about whether you are spending enough time in the sun and taking a B-12 vitamin. I have read that a darker skinned person may need 3 hours per week to get the recommended amount of vitamin D, a lighter skinned person 45 minutes.
- B-12 is 10 micro-grams per day. I personally take a daily B-12 vitamin as I can't always check the soy/almond milk I drink in my coffee and so have no realistic idea of how much I'm consuming per day. There is no harm in exceeding the recommended amounts of B-12.
- Vitamin D is 200-800 IU per day. You can cause harm by taking too much vitamin D so check any other vitamins you may be taking and the fortified foods you consume before resorting to another supplement.