Upvote:3
Yes, you can apply at any time.
However, if the application asks whether you have been refused a visa before, you must now answer Yes and provide an explanation.
It is important to remember that if you consent to receiving notices from the Australian government by e-mail, you are deemed to have received it on the day they sent it. Therefore it is your responsibility that you provide a correct e-mail address, configure spam filters so that those e-mails do not go into spam, and check your e-mail regularly.