Welcome aboard, Andrea! What a lucky daughter you have to receive a Disney Cruise for her graduation gift! That is a real treat not only for her, but for the whole family! I do hope you'll find the right sailing for your family!
If you're willing to give her the gift but not actually set sail until a few months later, you'll find a much better price on the cruise. Summer is peak season and prices do tend to be higher then, so my family loves to sail in the winter when we can find great prices on even the longer sailings, especially aboard Disney's two smaller ships, the Magic and Wonder. Both of those ships will be doing shorter sailings if you prefer the four-night itineraries, in the fall and winter of 2014, out of Miami or Port Canaveral. Sometimes you'll also find some great rates in January and February for longer sailings of maybe 6 or 7 nights on those ships too, however the 2015 itineraries haven't yet been released. The Dream does shorter sailings of 3 and 4 nights, however this larger ship does tend to have higher rates.
I'd suggest playing around with the
reservation tools on Disney Cruise Line's website. Try a few different months, length of sailings, itineraries, and see if you can find one that would work best for your family's schedule and budget. You might not set sail immediately after she graduates, but planning the cruise is half the fun anyway, Andrea!