I don't think IVF is a reason to be induced early (and 39 weeks is still early). If it were me (and I had IVF and went post-dates) I would refuse the induction unless there was some reason for it.
I was induced at 42 weeks with DS and I kinda regret it still. He was fine, not overcooked at all and my placenta was ok too. That's me, everyone is different of course, but if you're being monitored and there are no other complications then it's probably not necessary. And an unnecessary induction is only likely to cause even more problems for you. And, the earlier you have the induction the more likely it is that you'll run into trouble because your body just isn't ready. If there are no signs of readiness then you're not really 'favourable' for induction anyway, so the risk of ending up with a ceasar is greatly increased.
My induction was 'ok' - DS went into distress and I had to have a forceps delivery.
I think the most important thing is that you make the decision yourself and are happy with it. Don't get pushed into anything you're not comfortable with, kwim?

All the best to you