39 weeks pregnant and not sure if I will go into labor on my own =[?

I'm sorry. I was 2cm dilated for almost a month before giving birth, and baby was engaged as well. This does not mean you will not go into labor, but it does not mean you will either. No one can tell for sure --only baby knows ;) It does sound good though. Don't go trying all those old wives tale (walking a lot, taking castor oil, etc) ... only one thing can really work : sex (there is something in the sperm that might help you) and relaxing. Get all the rest you can so you'll be in great shape when the big day comes.