I cant speak for SA and how they bill/charge but in Victoria:
Water is already on and bills will usually default to the name recorded. At settlement I expect your conveyancer will change into your name. When a tenant moves in (that's if they pay for water usage) then they (or agent) contact water company and transfer into their name. The owner continues to pay service charges. I know in some other states the owner/LL pays for both service and usage. I always make a point of checking the water bill to ensure that I am not paying for usage charges.
With electricity, if you want this to be on then you need to contact the electricity company to switch this on, but there is usually a connection fee added to your first bill and typically a 1-2 day wait. That is unless the former tenants/owners have left it on but most will have this disconnected as soon as they move out.
With gas, I don't believe it actually gets shut off but I'm really not sure (best to check). I assume this is for your stove. There could also be charges involved to get the bill into your name. Again, best to check with the gas company.