Unless you are a casual employee the National Employment Standards sets the minimum for the personal/carer’s leave you are entitled to. This is 10 days per year, and it accrued over time – so, after a month you will have almost a day’s leave accrued, and after 6 months you will have 5 days leave etc.
If you are sick and you have accrued paid leave, your employer must let you take it provided you provide sufficient certification of your illness, such as a doctors’ certificate.
Your contract of employment cannot override the National Employment Standards – these apply to every employee in Australia.
If you do not have enough accrued paid leave, your employer may let you take unpaid leave, and is prohibited from dismissing you if you are temporarily absent from work due to an illness or injury.