Don't let "Nervous Nelly" keep you and your daughter from seeing some beautiful sites and having your own adventure!!!
I've never been on a cruise (not the crusing type here) but I have been "on my own" with my daughter as a toddler until now when we travel sometimes. We often tag along with hubby when he heads to a nice place for conferences, etc.
Just this past Oct., I stepped outside my box in AZ when my daughter wanted to go hiking in the mountains. We got a little sidetracked on the trail and our 3 mile hike ended up around 8 miles but we had a great time and still talk about it.
My brother and his wife go on cruises all the time and take their children everywhere (13, 10, 2). They love cruises.
Jamaica is beautiful. I lived there one summer, except I was not on the tourist side, I was in Kingston which was not the place for tourist. We did experience a wonderful time.
Enjoy!