Totally safe. We took our then 16 month old on the exact same cruise you are going on. It was very hard, I won't lie to you, but it is doable. The hardest parts were naps & bedtimes (2 naps a day at an hour or so each and bed at 8) did not make for fun times for whichever parent got to sit in the little bitty room!
I have written long e-mails to other people on this list about "what we did" and "what to bring" and would be happy to share those with you. E-mail me at ____@____.com if you want them.
With all the kids and family though, you are sure to have a great time! I say book it.
Good luck!
M.