We took our girl to Cuba when she was 11 mths old, she had a great time! Granted, summer days in Cuba is very hot and humid, very typical tropical climate. So make sure you put sunscreen lotion on her all the time, together with a hat! And leave clothes on your child even if she going into pool or by the beach, just keep clothes soaked to cool him/her. If possible, let her play under a beach umbrella, and avoid the outdoor during 11:00-16:00 when sun is at its peak.
You'll also want to bring lots of bottled water (they are expensive there)! Our girl was still napping twice a day then, so we couldn't go far, we stayed at the resort most of the time wandering about... Have fun!