A wool rug is probably the best and most natural choice. It is soft while being made of completed natural fibers with no chemicals added typically.
Carpet squares are something else to consider. You can put them together to form an area rug. The value of carpet squares is that when your little one decides to spill something on it or has an accident of some kind, you can simply pick up and replace the square (2'x2' typically) rather than trying to get the stain out. Products like the Ecoworks line from Shaw are a very environmentally friendly option for carpet tile.
Look for the Carpet and Rug Green Label Plus certification on any carpet you buy that is not a natural product like wool.
For more information:
Read "For a baby nursery, is refinishing the hardwood floor better than installing new carpet?" a Q&A answered by Martine Paquin.