I think you should consider renaming peanut and calling him/her coconut...

My SIL is TINY. She's Phillipino. My brother is 1.95m (sorry, not up with feet and inches). My mum is 1.72m, Dad is 1.83m, but SIL is 1.50m. Even with high heels she barely reaches his shoulder. Her son was 3.2kg, so quite big for her size. Unfortunately I can't report about a trouble free natural birth here, he ended up pushing onto her kidneys and they were impaired. The noticed at 38 weeks. She had a healthy baby boy a couple of day later, born through the sunroof (they were worried she wasn't strong enough for an induced labour, due to the impaired kidney function).
But, her mother had 4 children, all over 3kg, all born naturally, no drugs or intervention. Her father was just as tiny as the rest of them, so it seems that big babies run in her family and are not necessarily caused by my family's size.
Nt sure why I'm telling, you... just found it interesting.

Good luck with your birth DD!

Saša