The last I heard (please search the forum since parent visas have been discussed before) I think you can apply for your parents visa after you are 'settled' in Australia but the 'settled' bit wasn't really specified. I think it means such as things as a house, regular income etc.
My parents did consider moving here from the UK and spoke to an agent about it. They were told that the non contributory parent visa would take about 10 years but even the contributory visa could take about 3 years which would mean that they would be in their mid-70's before moving over and so they decided to stay in the UK. The contributions are large because you get immediate access to all the benefits here.
As Faisal said get some advice from a professional since things may have changed and their advice is based on your personal circumstances.