Yes, you can get the citizenship after you have spent some of your time on PR in this country. Talking about the time which is needed on the PR, its approximately, 1 year. However, you must have spent, 4 years, on a temporary residency visa in this country which can be a study visa also but the last 12 months of this time must be a on PR visa.
Now, when you are on a PR in this country, only 9 months residence is necessary out of one year. So, after living in this country 1 year on a PR visa and prior to that, 3 years on a temporary visa, you can get citizenship.
You will be happy to know that the fee for this visa is really minimal which is 285 AUD. Without a 4 year residence in this country, citizenship is not possible. After application, you get to know whether you have been selected for the interview for the citizenship. There can be a test(Australia Citizenship Test) also to grant you with the citizenship provided you are between the age group of 18-60.
In this test, there are varied kinds of questions which include whether you know, the English language well and questions about Australia.