If you are travelling with a dog through the centre, the only place in Alice Springs (I think) that is pet friendly is Heritage.
Please be aware, that our visit was cut short in Alice because of a very bad experience with uncontrolled and not supervised barking dogs in the park.
If you are staying in Alice with a dog and need to go to visit National Parks etc, I suggest you put your precious mutt in a dog kennels (or have him put down, joking.) and stay anywhere else but here.