Hello and welcome to the RTA forums !

As glc pointed out getting local advice is best but to be honest you don't have anything to be unduly worried about, millions of people/families camp out and don't ever see a snake or a spider. I am sure that if there is a particular problem of any sort in any given area there will be notices and leaflet advice all over the place.

Most camping is done in designated areas and a permit would be needed in most parks to do back country camping and even then you can't beat the experience of the local rangers for advice on anything you should be aware of.

Have fun !