Horns, there is an ongoing discussion in this section of Dunn's River Falls. If you look down the list of subjects in Caribbean Port Chat, you'll see that topic a few lines down.
There are those who say only the sure-footed and brave should climb the Falls under any circumstances. Others say it's a lot of fun, despite walking up the falls on slippery rocks with the falls, well, falling on you.
If you are tending to act on the conservative side since your wife got pregnant, I'd take a pass on this tour this time around and decide to do it on a future trip. If your wife is "showing" by the time of your cruise, it's possible that her balance may feel unfamiliar under normal circumstances, not to mention while climbing up a rock wall.
If she's really wanting to do the climb, at the very least I'd encourage you two to talk to her doctor about it first.
This is something to run by her doctor or midwife. It's also a good idea to have a signed note from him/her indicating your wife's due date and that she is cleared for travel. You never know if they'll ask to see it.
I would also second that advice. The rocks are very slippery and very steep to climb in spots. (there may even be a disclaimer about pregnant women not participating, I do know there is something about people with heart conditions)
Hope this helps!
I just returned from a trip to Key West, so I am a little late jumping on the bandwagon - but, I must agree with the other posters. I am definitely a "risk-taker" but would not take a chance on climbing the falls 3 1/2 months pregnant. There are just too many opportunities for accidents that would endanger the safety of your wife and unborn child.
just wanted to add that you can climb the actual falls, while your wife can take the stair route along side the falls. at 3 1/2 months, she should be able to handle the stairs easily. there is no water or treachery involved. plus, she can get some great photos of you in the falls.