Hi,

If you and your baby are keeping good health and you have no medical problems like diabetes, hypertension etc there is no need for induction of labour now.
The very fact that the cervix is soft means that you may start labor naturally in a week's time. Unnecessary induction itself can increase the possibility of you ending up with cesarean section. Induction of labour should only be done when benefits outweigh the risks of continuing pregnancy.
If I were your doctor I would wait for one more week. If you don't deliver by 40 weeks pregnancy, then I would do internal examination to try to separate gestational sac membrane from the uterus wall (sweeping of membranes). This sweeping releases prostadlandins which help in initiating the labour. I would induce labour at 41 weeks if not delivered by then.
I hope I have answered to your satisfaction.

Well, if the pregnancy is 39 weeks, it is very safe for the child to be born. If the cervis is soft, she will go in labour naturally.
The obstetrician's statement that if induction does not work, cesarean may be required suggests that probably your obstetrician feels that the mother's birth passage and the baby's head are matching each other in size only borderline. Probably that is whay he/she feels that early induction is indicated and if it fails, CS may be required.
During induced labour, the obstetrician will keep a watch on the welbeing of the baby and mother and if and when it is felt that baby or mother is not safe in labour, CSection will be done.
Induction of labour per se is not dangerous to the baby when the baby is fully nature.
The baby gets fully matured at 37 weeks of pregnancy. So at 39 weeks, there does not seem to be any danger for the baby due to induced labour.