Sounds like you have a lovely holiday planned & the Caribbean has always been my favourite place to holiday, so have fun!
I think others have given you good advice for managing type 1 diabetes on hols with a child that wants to be active & partake in everything. I would definitely second the benefit of investing in a Freestyle Libre for your break, it will make it so quick & easy to check on what your daughter's blood sugar is doing with no inconvenience to her whatsoever. It will also give you a snapshot of trends on the scanner, so you can easily identify any high/low trends at specific times in a different environment with different food options.
When I started using the Freestyle Libre a few years ago, I initially struggled with getting the sensor to stay on my arm, which was a rather expensive way of managing blood sugar when it would only initially last for 3-4 days!. However, when I discussed it with Abbott, they advised that the hot & humid conditions I love & swimming meant that I needed a stronger adhesive to keep it stuck on. Therefore, if you do decide to invest in the Freestyle Libre for your daughter whilst on holiday, it would definitely be worth getting some Torbot Skin Tac wipes to wipe on the skin before applying the sensor, so that it definitely stays stuck on & you can get the full benefit & value of the Libre.
Plus lots of people have mentioned about how hot conditions can lower blood sugar.....I have always been the opposite and freezing cold conditions represent hypo risk to me, so just play that one by ear, as we are all different.