It is australia wide.
All employment laws apart for government employees are covered by fair work.
You can have her sign that she acknowledges what has been discussed.
You should also be working with her to improve her work and give her an idea about what is going wrong.
Here is some information.
Yes it is allowed.
Here is the small business dismissal code that you should read to make sure you do everything right even though she cannot sue because any termination will be less than 12 months.
This is important in any dealings with your employees.
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