Note that character breakfasts are not offered on all cruises and when offered will not be an option each day. As PP mentions, BBB would be a good option and you can plan that for any given day (note that Pirate Night I think BBB does only pirate league makeovers). Royal Tea will be on a set day, but it is a very special thing to do. Maybe allow her to pick the excursion for that day (if it's a port day). You can order a birthday cake and it will be delivered at dinner. What did you have in mind as "more private?"
If you really want private and VIP, I believe you can arrange for a private meet & greet, but that is going to cost big bucks (maybe ~$1K). I don't know that there is much in the way of special events or private activities you can plan/book. I would just plan to spend time with her doing the things she chooses that day.
Enjoy your cruise!