Yes, that's possible. You'll have the option to invoice your customer in QuickBooks Self-Employed. Please ensure you have selected the correct region so you're currency is in Australian Dollar (AUD). You can go to the Settings and toggle on the Invoicing feature if you don't see this option in the menu.
Here's how to create an invoice:
Go to the Invoices menu, then Create invoice.
Select an existing or create a new customer and enter their information.
Decide when you want to be paid and set the date in the Due date field.
Click Add work if you want to add an item to the invoice.
Choose Flat rate, By hours, or By item from the dropdown.