Can't speak about the crowds or weather in mid-June (we always go the last week in May), but I'd say an 8-year-old girl could have the time of her life at WDW without going near a princess. Most of the rides and shows appeal to both sexes and all ages. Animal Kingdom has the Kids Discovery Club (a series of activity stations), and Epcot has the Kim Possible World Showcase Adventure (an interactive quest using a handheld electronic device).
My advice: Get a guidebook or two and let her help set priorities for each park. There's no way you can experience everything at a park in one day, so priorities are important. My favorite book on WDW is the Unofficial Guide, which is the size of a small dictionary and packed with information. If you'd rather have lots of pictures than lots of words, the UG also puts out a Color Companion to WDW, with over 500 color photos. And of course, keep reading the forums here for up-to-date advice.
