The Dream has lots of new innovations and seems to be a great ship for teens, so I am sure your daughter will have a great time.
You can order a birthday cake on board, or on-line prior to boarding. You choose if the cake is to be served at dinner or delivered to the stateroom. Carnival also has some birthday room decor packages that you can order on-line.
For a surprise birthday present, and to keep from lugging wrapped gifts, why not surprise her with a "swim with the dolphins" day or some other port activity.
You can pre-order customized tee shirts for her birthday as well. Be sure to tell the waiter that it is her birthday so they can sing to her at dinner, and get a birthday call out to her on the daily morning show on-board as well.
Been there - done that:
2005 Holiday, Sensation, Conquest,
2006 Conquest, Celebration, Holiday,
2007 Freedom Grand Med, Holiday
2008 Fantasy & Sensation,
2009 Fantasy, Holiday & Dream Grand Med
2010 Fantasy and B2B Elation
2011 Monarch of the Seas
2012 Booked - Breeze from Barcelona 12 days