The world is not a dangerous place, despite what the news might make you believe! Yes, there's crime, yes, there are some dangerous elements in the world, but these shouldn't stop you from exploring those places with your own eyes. Here are some tips that might help you be, or at least feel, safe.
Pickpockets can be anywhere (probably more in the crowded streets of cities than in the outback), the best way to prevent being 'pickpocketed' is to have your most valuable items in your front pockets (even better is if you don't have any valuables with you), which makes it harder for pickpockets to do their thing unnoticed. When there's a spot where a lot of people are huddled around something, or someone, watch your pockets carefully. These distracted groups of people are easy targets for pickpockets.
Furthermore, spread out your important bank cards in case you fall victim to one of those pickpockets, you always want at least one back-up card for essentials. Also in line with this last bit, scan all your major documents and upload these to your e-mail account, or to a USB stick. In case your things get stolen you can always fall back on your copies.
Get insurance! Mainly to cover any health issues you might experience, but insurance against thievery could also be useful. Always make sure that you have insurance before leaving!
Don't sign anything without reading the famous fine print. General terms & conditions for services can vary significantly from what you are used to back home.
Don't leave your things unattended. You might think "DOH, of course!", but it happens more often than you'd think that you leave something behind in good faith while you run to the toilet. Saves you some trouble if you leave it behind, but can also cause you a headache if you come back and discover it's gone. Besides losing material things, leaving your things unattended can also have other consequences. At a bar for a great night out? Watch your drink at all times, some people find it 'funny' to add some extra ingredients when you're not watching. You probably won't quickly forget your luggage at the airport, because the friendly people responsible for the announcements are happy to remind you not to leave any luggage unattended.
Watch where you walk (or swim)! The wildlife in Australia can be as beautiful as it can be dangerous. A lot of people are really frightened by the spiders, snakes, crocs (the animal, not the shoes) and sharks (among others), but the recorded attacks are so few, that it's not even worth mentioning the numbers. You're more likely to get hit by a car, or drown, then die from an attack of Australian wildlife. BUT, in order to prevent being attacked, always watch where you're going since most animals only attack when they feel threatened.
Avoid too much UV light. This is of course really hard if you want to go outside and explore the beautiful country, so protect yourself from the UV: use the slip, slop, slap, sleek and slide method.
If you want to take a dip in the ocean, make sure that you stay between the flags, which mark the parts that are being monitored and therefore are the safest place to swim. If you do find yourself in trouble while you're in the ocean, stay calm and try to signal to the beach by waving and making some noise.
Just remember that you need to see something with your own eyes to judge it properly! So always just stay calm and use your common sense and i'm sure that you'll have the time of your life while traveling!