Hi. At surface level, inducing at 36 weeks sounds like a great idea - aviod compressing your lungs and you get to meet your baby earlier! BUT...
There are several issues here. First, you can't be totally sure that baby will not have issues breathing when born at 36 weeks. The amnio is a good guess but no test is 100%. So while your breathing might be better, you up the chances of your baby ending up in the NICU with breathing problems of their own.
Second, You risk your baby having feeding difficulty from being born early. This is especially problematic with regards to breastfeeding. Most babies born at 36 weeks will do fine but you do increase the risk of that problem.
Third, I suggest you read up heavily on inductions. The main risk factor for an induction is an increased risk of c-section. I don't think anyone w/ CF would want to put themselves through a c-section unless it was absolutely necessary. Its major surgery and then you have to recover yourself while trying to take care of a newborn. Not to mention all the coughing...
If you plan on having any more children then having a c-section this go around will almost guarantee you a c/s for the next one. Its getting harder and harder to find a provider who will do VBACs. My SIL had a necessary c-s for her first and now pregnant w/ her 2nd had to switch to the ONLY OB in town who will do VBACs. And we are not a small town.
Fourth, as a first time mom, the likelihood of an induction actually working at 36 weeks is probably quite low. Do some research on "bishop's score".
I was induced w/ my son at almost 40 weeks. I will never do that again. It wasn't hell but it wasn't fun. Looking back I was lucky to avoid a c/s. I was not a good candidate for induction but my high risk doc wanted me to deliver by my due date and my regular OB did per her request. He didn't actually want to do it and I didn't know any better so I just went along with it.
If you are concerned about compromising your breathing, why not take a wait and see approach. I know you like your OB and she has experience w/ CF women but if it were me, I'd be looking for another provider. Many (most) OBs are VERY medically minded (my high risk OB comes to mind) but that may not be in your best interest. The best thing for the baby is to let him/her come when they are ready. Obviously if you start having problems then you need to reevaluate the situation. But routine induction at 36 weeks sets off red flags for me.
Please get the book "<b>The Thinking Woman's guide to a Better Birth</b>" by Henci Goer. It is a must read and if you are only going to read one book about childbirth, read that one. A hospital or doctor's view of "informed consent" is not really informed consent. The book outlines most of the interventions you may encounter and tells you the risks and benefits to each one. So if you decide to go ahead with interventions like induction, epidural, pitocin, etc, you will at least have a clear idea of what you are getting yourself into.
I know you are still early in your pregnancy but also look into writing up a clear birth plan of what you want and don't want in labor and delivery. And make sure you discuss it with your OB prior to the big day. Reading the book I mentioned will help you decide on your preferences.