The reason that it's not in the Grand Canyon campground reservation site is that since it's below the Rim it falls under the jurisdiction of the Backcountry Reservations Office>aka the BRO
You will need what is called a back country permit for this overnight stay
Indian Gardens [NPS code CIG ] is in the part of the Canyon that the NPS calls the Corridor and such except for the period from11/15 >2/28 you are only allowed 2 nights total at any given Corridor CG [from11/15>2/28 that # expands to 4 nights total ]
Most hikers use CIG as a place to
Break up a long hike a cross the Tonto
A legal CS to use if you get a late start on your downhill run
A place to spend the night before you begin your long uphill hike out of the Canyon
I used it once coming from Clear Creek heading to the Rim
Needless to say it's a really popular CS and you will probably have trouble getting space this year
Have a safe hike
Oh yeah before i forget
http://www.nps.gov/grca/planyourvisit/backcountry.htm