don't worry about it, I've had dogs all my life and none have ever been bitten by a redback, redback's aren't viscious, they will leave you alone if you leave them alone. Most people get bitten because they don't see them when doing something in the garden.
The older perth areas rarely have them, where I live we have them but it really is not a problem. We go red back hunting a few times a year at night and kill them all. We find the best way to kill them is with a shoe, the spray does not kill them immediately, so there is a chance your dog would come and examine it when it falls to the floor, so make sure you kill them outright.
The best thing about perth is that it's a great safe place to own a dog. We all have enclosed yards so our dogs can be outside when they want. If you have a small dog you can even have a flap so they can go outside/inside by themselves.