There are a few particularities to watch out for regarding traffic in Australia. First of all, there's left-hand driving and in urban areas you will often be confronted with a round-about. Highways and country roads are usually double-tracked at the best with strategically located parts for overtaking. You will only find highways with multi lanes in and around the big cities. Overtaking on the wrong side is common. It is not permitted, but obviously drivers ignore that. The police, however, is very strict when it comes to speed limits. The general speed limit on rural highways is 100 km/h and you should strictly stick to that. Speed is often measured via radar devices or directly from the driving police vehicle. Highways are not fenced off, so there might be a flock of cows on the road after a turn. Watch out after dark also, because then the kangaroos get active. Those can leave considerable damage and are often, although not always, just very dumb! So don't think that they will clear the way when they see you coming!
You should carry an International Driver's License! Although car rental agencies hardly ask for a translation an International Driver's license is mandatory. You can apply for your International License in Germany for about 15 EUR.
You will find Rental car agencies in every bigger city. A lot of smaller companies are in competition with the big agencies and if you grant yourself some time with finding a car, you can find a bargain. Usually you will only be able to rent a car if you are over 21! Often there is also a maximum age limit and with many companies that is 75. If you book early at Australia's big ones -Hertz,Avis, Thrifty - it usually is cheaper. The average price for a small car is around 70 AUD a day. The smaller rental car agencies often offer prices of 30 or 40 AUD a day. Rental contracts usually have a clause that prohibits you to drive on unsecured roads. Almost all national parks and natural sights can only be reached via gravel roads. If you should have an accident on one of those roads your insurance will not cover it. You can rent a car with only a German Driver's License, but you are legally committed to carry an International Driver's License.
Buying a car to be mobile in Australia is a very good alternative to renting a car. Additionally, it is quite uncomplicated: find a car, sign the contract, get car insurance and go! It is, however, hard to go looking for a car without one. "Backpackermobiles" are certainly the easiest way. But often these cars have seen quite a lot of Australia already. Obviously a car maintains considerably longer in Australia compared to Europe. Good used cars with 170.000 - 280.000 km are not rare. Unfortunately, they are not cheap either.