Do I need a voltage converter?

Yes, it's multi voltage so you'll only need a UK» US/CA travel adaptor

I'm afraid tentofield has misled you slightly. It is not just a question of voltage. I have here a transformer that drops 240 V down to 115 V. It weighs just over four pounds. The output is 0.35 amperes at 115 V. AC. That means it can handle 115 times 0.35 or 40.25 watts. That would be plenty to run your laptop or phone charger but there is no way it could handle a hair dryer. It might be able to handle a hair straightener, a small one that draws 35 W or less. This is a transformer, a simple but heavy device made of iron slats and two copper coils. To run a hair dryer would need a much bigger and heavier transformer, possibly weighing 25 pounds or more. Now if you look carefully at your phone charger, it may have a label that says it is suitable for 100 to 240 V. The output is 5 volts DC. Mine has that label. Your laptop charger may be similar, but check the label or any book that came with the phone or laptop. If they have this label, all you need is a plug & socket adapter. The difference is that the internal circuits are intended only to produce a very small direct current and a transformer is not needed for that, just a few small diodes and a voltage regulator. You will find that most medium to higher priced hotels and motels in Australia have hair driers wired in or available from reception. So don't bring your own. .

It uses the same current. You should be fine :)