The best trip I've had with my baby was when she was ten months old. We and a large part of family on my Dad's side, rented a few condos in Kauai. We stayed for two weeks and everything about it was memorable. It was our first real vacation with baby Brooklyn and we were more than nervous. Once we got there, all our fears were set at ease.
The way the Kiahuna Plantation is set up, the condos are all in a 'U' and it allows for a large, sheltered field to be in the middle of the grounds. There were trees that offered a lot of shade for her delicate skin, and with all of us staying right there, there was always someone watching over her. The water was perfectly warm and it wasn't too hot, so she had a phenomenal time experiencing all the new textures and scenes.
I would highly recommend a Hawaiian escape to any family! Especially Kauai, as it's very low key there with a lot less people than the neighboring islands, which we all liked.
Have a look at the video on Kauai below. Some of it is filmed on a rainy day, but Kauai is beautiful even then!