Of course... how is that different to the any fund manager/share trader who trades for a living, but also invests his hard earned.
Just because you might run a share trading business, doesn't preclude you from also investing in a private capacity.
I am assuming you know the criteria for being recognised as a trader. It doesn't just mean holding an ABN by the way. Sadly, there are a lot of people who falsely assume just because they hold an ABN they are a share trader... simply not true.
You should look at the strict criteria the ATO enforces.