Hi canuck_at_large
Good advice by Luigi regarding the dangers of walking in this area during the summer months.
Do not take notice of his Elton John- style conformity, as his advice is crucial!
Your biggest concern should be- is to ensure that you have enough water with you, have a Sat Phone and advise local authorities and family, of your departure and an ETA, in case of an emergency.
It is less than an 8km walk from the Kathleen Springs car park, off of Luritja road.
From memory, you will need to head back down and cross a few creeks including- Kathleen, Wanga and Reedy creek which will head towards Watarrka, (Kings Canyon) car park.
I would never recommend hitchhiking- but that part of the trip is totally up to you.