Let's get the easy question out of the way first. Yes, you will need to buy your ticket to South America before you depart for the US. One of the conditions of entering under the VWP is that you have either a return or onward ticket out of the US within 90 days of entry. This will normally be enforced by the airline, and if you do not have such a ticket you will likely be denied boarding of your flight to the US.
As far as your "visa run", the short answer to this is "it depends".
Technically when you leave the US and travel to a country other than Mexico or Canada (or some locations in the Caribbean) your current VWP entry will end, and when you re-enter a few weeks later you will be given a new VWP, with another 90 days of validity.
However, as with any time that you are entering a foreign country, it is up to the discretion of the the immigrations officers as to whether they will let you into the country, and they can ask you any questions they wish in order to determine your intent.
If, in the opinion of the immigrations officers you are either intending to stay over 90 days, and/or if they believe that your 2 week trip to South America was simply done as a "visa run" in order to extend your VWP status within the US, then they will almost certainly deny you entry. This could happen on your first entry to the US, or on your second entry.
Even if they don't see this as a "visa run", I would expect them to question you over what you are doing in the US for 6 months, and how you intend to financially support yourself there without working - which is not allowed on a VWP visa.
As annoying as a trip to Perth (or Sydney, Melbourne or Canberra) to get a visa may be, in this case I would strongly recommend it or you may find your trip to the US cut short.