I say go and have some fun!
My DH and I are going to Mexico, even though we will be in our second trimester by then if things keep going well. We are taking a cruise out of L.A., which works better for us that trying to do a long flight and booking hotels. (Yes, we bought the insurance as well!)
Something I've learned from years of travel - even though it is a tropical location, it is still Jan/Feb, and the weather is still a little cooler. Bring clothes you can layer in case of rain or chills. (Our last trip was in early Feb last year and the weather was constant drizzle except for one or two days. Warmer than Seattle, but still not the perfect April/May sunshine!)
Like you, I won't be drinking, horseback riding, etc, but there are still lots of fun things to do, like shopping, exploring, meeting people! Gambling away our child-to-be's college fund!
Have a good time and enjoy yourself!