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In the circumstances you describe you may well be able to sue your landlord for your injuries, which means suing for compensation. Of course to succeed you need to prove that your landlords negligence or deliberate improper act caused your accident. Two ways appear as possible grounds for alleging liability. One, that by interfering with your or your agents lawful access to your premises they caused you to have to go out when you were in no fit state to do so, or alternately, the uneven stairs likely do not comply with the Australian Building standards posing a foreseeable risk of injury.
Only a personal injury lawyer fully briefed in the facts can give you firm advice, but based on many years dealing with similar claims in the insurance industry, I suspect from your story that you will have a viable case.
If you need help locating a suitable lawyer, contact the Law Society in your state, called the Law Institute in Victoria.
I trust the above assists.
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