Does an employer have to pay superannuation on top of bonuses or can they pay it out of the bonus?

It depends how the bonus conditions are written. It is quite common to pay it as “inclusive”
Speak with someone in your payroll or get out your bonus agreement

Hi Luke,
the correct answer is "it depends"
and what it depends on is whether or not the bonus is classed as "Ordinary Times Earnings" or not.
If the bonus is as a result of what you do in the ordinary course of your work, then it IS subject to Super Guarantee
eg, Chistmas Bonus, Performance Bonus, etc

If it is in respect of work performed entirely outside your normal hours, then NO super
eg Overtime Bonus

this might help
https://www.ato.gov.au/business/super-for-employers/in-detail/ordinary-time-earnings/ordinary-time-earnings-and-super-guarantee---examples/

best thing to do is TALK to your employer and find out what they think is the way it is, then if you dont agree you should come prepared and explain why you think it should have super on it

good luck
bc