Australia is a safe country where safety problems are rare. There is petty crime, like everywhere in the world, but generally speaking nothing is likely to happen to you during your travels in Australia.
Australia really is a safe country and the only things that might happen to you are the same as in Europe. So, watch out for thieves and pickpockets on public transport.
Violent attacks are extremely rare even though the risk exists. These sorts of things are most likely to happen in big cities where certain areas and places that are too isolated should be avoided. This also applies outside the big urban centres The Outback and the centre of the country have their own dangers. The Aboriginal community is seriously affected by problems of alcoholism. Attacks are more likely to happen after nightfall.
If you're hoping to buy drugs or anything else illegal, you'll bring yourself into contact with the sorts of people who should be avoided. Just because Australia is safe, doesn't mean you should be reckless. However, this isn't a sermon, you're a well-informed, intelligent person and you know the score!
Just take the same precautions as you would at home. As a general rule, so as not to attract the attention of muggers and pickpockets, try to blend into the background and avoid looking too much like a tourist. Be particularly vigilant on public transport. That's where you're most at risk. Take care after dark too. For example, avoid quiet parks and particular neighbourhoods. If you are mugged, don't play the hero. Don't offer resistance, stay as calm as possible and give them what they want. It's also a good idea not to keep all your money in the same place. Keep it in different places, so you don't lose it all if you're mugged.
A special note about the towns in the centre of the country. The streets of Alice Springs are much less safe after dark. Alcohol is a big problem amongst the Aborigines and you may well be bothered by drunken individuals.