This probably deserves its own thread, because I'm sure there are lots of kids like your little one, who will be experiencing the Oceaneer's Club for the first time on other ships as well.
But since you asked here. . .
My daughter was also 6 on our first Disney Cruise. She is also an only child. She was also a reserved child. I wouldn't say she was clingy, but she would ALWAYS stand back and watch what was going on before deciding if she was going to try something new. Since it was our first Disney cruise and there were no cool message boards like this one, we had no idea what she was getting into. So (being extremely over-protective parents of an only child) we went with her and stayed with her for a while on her first day. That helped; although if your child is "clingy", it might be harder for her to let go.
I would humbly suggest that you try to get her excited about meeting characters. One of the great things about the Oceaneer's Club is that the characters come and interact with the kids for a long time. Belle will come in to read a story. Peter Pan and Hook will come in to play hide-and-seek. If she's clingy, she might not be interested in "You'll make new friends"; but my daughter was very happy to interact with all of the Club's "guests".
I'm sorry to hear that you struggled with health issues so early on; but hopefully, they're behind you now. Our daughter is an only child because of my
wife's health issues during her pregnancy. We did NOT want to risk that again!