Most high end deriviative jobs are in sydney. MOst stock jobs are in melbourne.
Kospi is shit IMO, nikkei has more of everything compared to the little whinger that is the kospi.
Most large broking firms all have offices in syd/melb MAN, Brokerone etc and will give you superquick access to asia pacific markets. Trading US securities is best left automated as time zone differences will mean that ull be up in the middle of the night or early morning.
Aus also has a very well developed CFD market allowing you ot trade everything from commodities to indexes using CFDs. IG markets is teh premier provider although new vendors are opening all the time GREENCFD etc. Most will require only a small minimum deposit to start off with and will operate synthetic markets. Bid/ask spread is poor on indexes and commodities but teh lack of a commision charge makes up for it somewhat.
Moving to higher end derivatives:
Local SPI has been the most faithful bitch of a market ive ever come across. Been trading it for 6yrs now and my strategy has worked year in year out, month in month out, week in week out. Out of all the markets ive ever traded SPI has yielded teh best profits by far esp in the past few years as volatility has increased.

hey i gotta plug my local market right? lol but seriously SPI's a nice market to trade.
There are also some fairly liquid markets in Commonwealth Bonds (3 and 10yr) and Interest rate securities. However if your trading bonds the Japanese bonds will probably be teh most deep and liquid markets in this region. Time zones are not too far apart. Wool and Electricity markets are also available but liquidity is extremely poor so they are best steered clear of.
Australian Equities are not that great for trading. Large stocks with good liquidity include most of the large banks and mining companies (BHP, RIO, CBA, NAB etc). If your looking to profit from speculative trading on stocks, your better off with using CFDs. Australian equities are however an excellent investment with P/E ratios in overall at low levels, and the dividend imputation system means that stocks can provide you with tax effective income.
Hope this provides you with a good overview of the trading opportunities in australia