I've done my hair 3 times since I have been pregnant and been fine everytime....I just used a no ammonia colour :)
As long is you're not in your first trimester
You can color your hair, yes. I wouldn't recommend dying it as dye is used for fabrics. When you color your hair or have it colored in a salon, just make sure you're in a well ventilated room. The only issue with coloring your hair is inhaling too many chemicals - there is no risk of the color seeping through your skin, etc... As long as you are up front with your stylist and let her know you are pregnant, he or she should make sure to seat you in a well ventilated area of the salon or at the very least, time the process so that you get to go outside every so often.
I got my hair done professionally my first trimester. It's fine. As. Long as you aren't breathing in the funds you should be okay.