U.S. and Canadian power mains supply 117 volts AC at 60 Hz (cycles/second) while Austrailian power mains supply 230 volts AC at 50 Hz. As you already know, your wall powered gear will not work without some help. What you will need to do depends on the gear.
Here's a link to some info about power standards worldwide.
Here's another from that page to Australian standards.
1. Many products, probably including the power supply for your computer, have a switch that adjusts the nominal input voltage range between 110 - 120 VAC (volts AC) at 60 Hz to and 220 - 240 VAC at 50 - 60 Hz. For any of your gear that has such a switch, all you'll have to do is move it to the correct position.
Be SURE to check the specified frequency as well as the voltage. Depending on whether the design of a particular power supply is linear or switching, this can make a huge difference because the efficiency of linear supplies is greatly reduced at the lower frequency.
2. Some power supplies have a "universal" design that accepts the full range of input voltage and frequency. Read the specs on each device.
3. For any gear that uses a wall wart, you will need to buy another one that works on the local power mains and delivers the same output voltage and current as the ones your gear currently uses.
One other word of caution -- Even for gear with connectors from the D.C. output that look and fit the same, there is NO standard for which contact (the outer sleeve and inner contact) is positive. You should know this before connecting a replacement supply to your gear. If the power is reversed, you could damage your gear.
4. For any gear that uses only 117 volt, 60 Hz AC, you will need a step down transformer with the appropriate plug to connect to the Australian mains that converts the power from 230 VAC at 50 Hz to 117 VAC at 60 Hz and connects it to a standard North American receptical.
This is the least efficient type of conversion so you should use it only for the most important legacy devices you need to keep. For any of your gear in this group that uses a lot of power (high power stereo amps, appliances, etc.) it may be best to consider selling what you have and buying new gear in Australia.