The quickest way from Brisbane to Rio de Janeiro (for example) is a one stop Emirates flight (31-32 hrs) via Dubai. (not redeemable with Velocity points). ~$1800 return.
To Santiago (18-19 hrs) via Auckland with Latam (not redeemable with Velocity points). ~$1600 return.
To Bueno Aires (18-21 hrs) via Auckland with Air New Zealand (redeemable with Velocity points???). ~$1800 return.
You may be able to still use Velocity points for Air New Zealand flights (I think their partnership is ending soon). Otherwise, you could transfer your Velocity points to Krisflyer to redeem Air New Zealand flights.
I know its a lot of money but I find with economy flights, its sometimes better to pay cash and fly the most direct flight. Economy redemptions, you still have to pay taxes/surcharges.
The alternative is try for Delta flights from Sydney to USA with Velocity points and then find your way down south. Not the most direct route.