We took our engagement photos with our wedding photographers, The Roots, at the Polynesian and Wilderness Lodge. It was included in our package, so I'm not sure of the price of just engagement photos. It was really fun, and we got some great shots.
To do them inside the park you have to use Disney photography - either through PhotoPass or by scheduling a $310 Honeymoon/Engagement Portrait Session through Disney Event Group Photography (407-827-5029). It takes place during regular operating hours. You get 20 4x6-inch prints in a leather-bound album and one 4x6-inch print of every image.
...OK, I can't resist adding a couple of our engagement pictures...