I'm the family cruise editor here. Yes, some lines do have wide age groups for kids while those which carry the most children annually -- such as Carnival and Royal Caribbean -- separate the kids into narrower age groups. Generally the youth counselors won't bend the rules -- if you're not 13 yet, then you can't join the teen program unfortunately.
Hopefully you'll have a fun time anyway. Princess is a really nice product with beautiful ships, great food and excellent service. Maybe your daugther will meet others her age to hang out with. I'd love to hear how it went upon your return.
Smooth sailing,
Luisa Frey Gaynor