Always best to let someone know where you are going. The Hungerford Road seems fairly well traversed, but a breakdown on the other roads may see you stranded overnight, so be prepared.
You need to carry sufficient supplies of water, food and fuel for the journey, and some in reserve.
There are snakes in the park, including the Mulga Snake, leave them alone.
Take care walking far from the road. The country, with its red soils and Mulga shrubs has a certain sameness which is disorienting, and the lack of any grass cover means that a track cannot be followed or marked effectively - the tracks appear to go everywhere.
There is no mobile phone reception for any mobile networks in the park.