As long as it's you, your money, and on your own account, then yes.
If you do it on behalf of somebody else, or, if you provide advice to others (however informally)
then you will need a licence.
Get formal advice from a solicitor and accountant about how to treat trading gains and losses
in terms of 8-1 (income) and CGT.
And no, you don't get to hide your trading proceeds from the ATO by operating cyber-overseas.
Lastly, beware of software packages that are not Australian-authored.
Stuff that's written to comply with, say, the law in the US
may not be the best choice for an Australia domiciled trader.