While there are some limitations on it, namely length of stay above six months, as an Australian citizen, you do not have to apply for a visa to enter the UK. You still have to carry the same supporting documents with you to show an immigration officer at the border.
But with your recent refusal I would not recommend doing that, and instead open a new question here with a scan of your refusal. It's very easy to focus on what you think is the most important part of the refusal, and subsequently, ignore very dangerous warning signs that are also there and may put future applications in jeopardy.
You can then use the advice given here to apply again, hopefully, this time successfully. This saves you not only the process you will likely have to go through at the airport but also money in case you are denied entry.