Driving in the Northern Territory - bad idea?

Hi,
Is driving through the Northern Territory a bad idea? My fiance and I
will be spending some time there and would like to visit Kakadu,
Katherine, Kings Canyon, Uluru, and the Olgas. We were planning on
renting a car, but hear it might not be so safe (in terms of speed,
getting lost, road-trains, and roaming animals). Is there anything to
see between Katherine and Alice Springs that would make the drive
worthwhile? If not, would it be best to drive through Kakadu and
Katherine, and then fly from Katherine to Alice Springs or Uluru?
Thanks.