It turns out that Elephant grass earned it name because it is a favorite plant of elephants back in its native home of Africa. It is edible for people too, and by extension, rabbits. Plants for a Future says the young shoots or leaves are added to soups. Elephant grass is closely related to millet.
According to Feedipedia, it is primarily used in cut and carry feeding systems and used to make silage. It is desirable due to its wide range of habitats and drought tolerance. The fresh leaves an stems are reported to have just 1-10% protein, but to be a good source of carotene. Historically there have been a few cases of nitrate poisining in cattle fed on exclusively Elephant Grass, but I remember reading the same for Tifton hay also. Archive has a fantastic book about using Elephant grass as a fodder crop in Hawaii.
It is also used to make thatch and mulch, and to prevent erosion if planted on contour.
Elephant grass is mainly grown in stands. It produces few seeds and is usually propagated by stem cuttings of at least 3 nodes, 2 of which are buried into the soil. Has been known to grow 4 meters in three months time after planting from stem cuttings.
It has been growing very well in my yard for almost one year now. I plan on taking cuttings out to the forest to plant on the sandy areas created by cars driving through the corner of the land.