induction at 37wks

B
My December baby is turning into a November baby. I'm going in Wednesday (11/23) to be induced at 37wks. Baby is small only 5th percentile so doctor is concerned about the placenta starting to fail. Has anyone been through this before? I know every baby is different but I'm just worried about how long she'll be in the nicu. I'm assuming she'll have to stay since at my last ultrasound she was estimated at 4.10lbs. I was only 5.10lbs when I was born so I'm hoping she's just a small baby and won't have serious complications. Doctor also keeps emphasizing how I may need a c section since the chances increase with pitocin and since she's so small she may not be able to handle the contractions. Just wondering if anyone else has gone through something similar and had a good outcome where baby didn't have to stay. I'd be heartbroken having to leave her.