Induction cons?

My goal was to have a natural hospital birth. I hired a doula to help coach me during the birth.  
But now my OB is saying they are firm about inducing by 41 weeks. (I am 40 + 3, 1 cm dilated and 80% effaced, so it is looking likely that I will see 41 weeks). Does anyone have any good resources to share about pros and cons of induction?
My doula is saying that I shouldn't need to induce yet and is strongly discouraging me to just go along with what the docs say, saying that they have poor reasoning for inducing. While I agree that my healthy pregnancy and baby don't need to be pushed, I am feeling pretty cornered. I feel like I have to advocate for myself with both my doula and my OBs. And yet I really know nothing about birth. Bleh.