If you are a permanent employee (eg. part time or full time) you are entitled to take paid Leave to care for your child if they are sick.
Personal Leave is the form of Leave available for the purpose of caring for a sick child. Personal Leave accrues each year, at the rate of 10 days per year for full time employees (pro-rata for part time employees).
This is the same form of Leave that you take if you are sick (ie. all 'sick' Leave comes off the same balance of 10 days - whether it is because you are sick or whether it is because you are caring for a sick child).
Employees are often required to provide 'evidence' of the child being sick to their employer upon their return to work. 'Evidence' includes production of a medical certificate from a Doctor. It is best to check your company's policy on this requirement before you actually need to take the Leave. It is acceptable for an employer to require a medical certificate for even a single day absence.
It is a good idea to familiarise yourself with the company policy / practice in relation to taking time off to care for children, or leaving work early to pick up a sick child - eg. is it acceptable practice to work from home for the rest of the day?
Ensure you are familiar with the child care facility's policy in relation to sick children - are they unable to return for 48 hours if they have had a temperature? Do they need a clearance to attend if they have a rash?
Importantly, ensure you have had a discussion with your partner upon your return to work and are in agreement as to the approach when you receive a call notifying you that your child is sick and you need to pick them up early.
Be honest with your Manager about why you are leaving early, or why you cannot go to work - let them know that your child is sick. If feasible, offer to work some time from home to ensure you can complete some of the work. You could even offer to work a 'make-up' day another day if possible.
If you don't have any personal leave left, then you will need to consider taking annual leave or potentially unpaid personal leave.
It's not always possible to leave work immediately and pick your child up, so it is good practice to have a plan in place on what you will do in this instance.
Perhaps your partner could take some time off or work from home to look after the child - you could stay home for half a day each, that way both having an opportunity to complete key tasks at work at some stage during the day.
Other options include building a relationship with someone you trust who could become a 'babysitter' for you. Find out if they would be open to looking after your child on occasion, if you were unable to take time off work, if they had a cold or a cough. You might need to find someone through an agency, or you might be referred to someone.
It's a good idea to establish this support network prior to returning to work as children often experience the highest volume of illness in their first year in a child care environment.