The main concern isn't the chemicals absorbing through the skin, it's what you're breathing in. I was told to make sure I was in a very well ventilated room if I'm dying my hair preggers.
It's fine to color your hair when you're pregnant. I'm a stylist and I'm 34 weeks and still working, pregnant women come through my salon everyday for color. The only thing is your skin might be more sensitive to the higher volume developers like 20 or 30, and like the other comment said coming out a different color. But I've never seen that happen.
One of the main concerns I was told with coloring hair is it not taking it or it changing to a completely different color like blonde to orange or red to purple lol. No one has said anything about the smells and it effecting the baby to me. They more worry about my hair turning a funky color lol.
Hair dyebis perfectly fine, it doesn't absorb into your skin. I dyed my hair twice when I was pregnant, at a salon so your fine. They have done a lot of research, just make sure your in a well vented room, I know you said ammonia free but that stuff can still get stinky :)