Don't think twice....go and have fun!! My husband and I took our son on his first cruise last year a month shy of his first birthday. We had some concerns but surprisingly he did really well! He loves to be out and about so having a new space (an entire ship!) to explore kept him entertained. During the day we kept him with us. On sea days we explored the ship (Navigator of the seas), played mini golf etc, and on port days we took him with us too. Again, we knew he wouldn't be any trouble because it's something new to capture his attention. We got him ready for bed and dropped him off at the nursery on our way to dinner most nights. He would be sleeping when we picked him up after an hour or two. The short time was due to me worrying about being away from him and leaving him with strangers, given that he cried every time we dropped him off.
We're booked for another cruise on Allure of the Seas Sept 15th. He's 2 yrs now so will see how that goes!