Hello there, NJ. There's still time for something to happen before induction becomes a reality. I went over by 2 weeks when I was having my DD - I had an appointment at the hospital on Friday afternoon, where I was told that I would have to come back the following morning to be induced. The doctor then gave me an internal examination. I went home all despondent because I really didn't want to be induced. That afternoon, at about 2pm, I had a show, which I attributed to the internal exam. Nothing else happened until 2am - I woke with a start when my waters broke and contractions started. So, I ended up going back to the hospital ealier than expected but did deliver on the Saturday, just under my own steam!
A similar thing happened with my DS. I was just over 39 weeks and absolutely felt that birth was imminent. I was fed up and didn't want to be pregnant any more! I had an appt at the hospital, where a rather brusque doctor told me that there was no way that the baby was going to come out and that he was going to put my EDD back by a week. Again, I left the hospital all despondent and even more fed up than when I arrived there! I got back home and, a couple of hours later, my waters broke. Again, I was back at the hospital earlier than expected and again delivered the next day (also a Saturday)!
So, what I'm trying to say (in short) is that you never know - your body may well decide that it wants to do its own thing despite what the medical professionals have planned for you. There's still plenty of time for it all to kick off before an induction is really on the cards. I'll certainly be keeping my fingers crosse for you!