I'm confused, too. Are you sure that the other person is a native speaker? Or, if they are, are you sure that you heard the first question correctly?
If the other person isn't a native speaker, I can only presume that they were asking you the 'wrong' question - in other words, their first question wasn't what they meant to ask you.
"How long have you been in Australia?" is asking you about the time from when you arrived in Australia until now. It's now the middle of February. So, if you arrived in Australia in late January, your answer is correct : Q: "How long have you been in Australia?" A: "I've been here 3 weeks". Is that correct? Have you really been in Australia since late January?
Unless the other person knew that this was untrue, their response of "No" doesn't really make sense. The second question has a different meaning. If they'd wanted to ask about the total length of your stay, their first question should have been "How long are you in Australia for?"