I'm a diver and have worked with training students before, so I have some questions for you:
How long ago was your transplant? How is your breathing now? What are your PFTs showing, and when was your last one? Have you had any readmissions to hospital, and what for? Have you ever had a pneumothorax - a leak from your lungs causing an air bubble between chest wall and lung tissue? Diving can be taxing - how much exercise do you do and how do your lungs handle it?
Importantly, are you planning to get certified at a dive center where you live, or are you thinking of a 'quickie' course at some tropical location? I would steer you away from the latter - their business is to get you in the water and with a dive card as quick as they can while your credit card goes through. A local shop in your town that takes a few weeks to train you fully will have more chance to work with you and ensure your safety. You will need very close monitoring during the training, and a zippy course at a resort is not set up for that. Remember if you have a problem the nearest medical center may not be too close, and have little experience with CF. I don't want to sound like a downer, but I have seen people without medical problems get into grief underwater, and you have a few extra risk factors here. To date I have rescued seven underwater, and don't want to see you become a statistic.
Take the time to do this: call the Divers Alert Network. They specialize in medical aspects of diving, and there are med staff there 24/7 to answer questions and advise. Their numbers are 1 800 446 2671 or 1 919 684 2948. These are both non-emergency numbers, though they do maintain an emergency line for diving medical help so people can call from all over the world and get help or medivac assistance from dive accidents. I have called them before, and they are the absolute experts on dive medicine. They will also take the time to address your questions fully. Write down anything you want to ask in advance and they will cover it all. My list of questions will be a good starting point.
If you are okayed, head off trouble by getting a friend who is familiar with your ailment to train with you and go on the trip. Dive destinations have first-aid trained divers, but aren't going to see many CF folks, probably none. Someone who knows you well and can answer questions in an emergency can be a lifesaver. Murphy's Law applies, if you are prepared to this extent, you won't need it.
If all goes well and you get your trip of a lifetime, make sure to come back here and tell others about it. You will give hope to people waiting for a transplant and wondering if they will ever have a life again!
Stay well, john