Yes there is LCC competition between SIN and SYD (as well as KL to SYD). It will be interesting to see how it all works out.
As I have written for next month’s Snapshot page, Southwest is a survivor because it’s controlled its seat mile costs.
Ryanair also keeps costs down even though in doing so it alienates some passengers with its way of doing business.
The key to success in the LCC business is keeping down the cost of seat miles.