I was able to reapply for the Visa and it has now been granted.
Here some more information what happened and what I had to do:
I applied online for a Temporary Graduate (Graduate Work) (subclass 485) visa. During the online application I was asked if I do have a police check. I clicked "No" and I did not get a warning and I could simply go on and do the payment for the Visa (What I think is pretty much a fraud if they let you continue despite the fact that you can not get a Visa if you clicked "No"). So I assumed I can just apply and upload the police check later like you have to do it with all the other documents, what I did two days later. (You can only upload documents once they received you payment). After three month of waiting (I assume that's how long it takes to realize that someone clicked "No") I did get the refusal letter (Because you have to apply for the police check before you apply for your Visa). By that time my old Student Visa had expired and I was on a bridging Visa giving me 35 days to leave the country (you can not apply for this Visa again if you are on a bridging Visa). So I went to a nearby (non Australian) island for a week and came back on a Tourist Visa. Than I could apply for the Visa again (with the EXACT SAME application they refused before [I had to add my week abroad of course]). And of course I had to pay for it again. After another three month of waiting, during which I could not work because I was on a tourist Visa, my Visa had been granted.
So yeah, be careful to apply early for the police check. They don't care if your police check is ten month old, that's okay, but if it is one day to new then they do care.