I was there in late august in 2002 or 2003 and we saw several moose on the western end of the island on the Feldtman Lake loop. However, that was when there were approximately 1100 moose on the island. Sadly, there are now only about 385 as of winter 2007-8.
I don't know how you are getting to the island, or from where, but I would recommend getting reservations for the ferry you choose. I looked into going last summer and of the two ferries docked in Grand Portage, MN only one was running to windigo because of the low water levels. The other boat was too big to get into the bay.
Once you make it to the island, the campsites are pretty much FCFS but we didn't have much trouble finding good campsites. Although if you're going to be on the eastern end of the island, its a bit more crowded.