A car is not a necessity. You won't really need it to go to parks, or Magic Kingdom related resorts (Grand Floridian, Poly, Wilderness Lodge, Fort Wilderness) since you can take monorail or boat (you can of course easily walk to the Contemporary). Where the issue of possibly having a car arises is if you want to go to Downtown Disney (buses go there but because of multiple stops, trip there and back can be very long), or go to a resort other than the ones mentioned above although you could still walk to MK and catch a bus to any other resort. If you want to do anything off-cite, go to a grocery store, off-site restaurant, Universal Studios, then having a car is a good idea.
My guess is that if this is your first trip it is going to be very park heavy and most everything else light, for which you won't need a car.