Are there any rules around the period of time that has to lapse between a job being made redundant (for genuine business reasons) and re-advertising for the same position?
There is no rule to speak of but you should consider that the closer together the two events, the more risk you have of the retrenched employee attempting to make a claim that their redundancy was not genuine, and thus make an unfair dismissal claim.
If the retrenched employee wanted to make such a claim and more than 21 days had elapsed from the date of their termination they would need to apply to the Fair Work Commission for an extension of time to lodge their application for unfair dismissal. Although not impossible, this would be some barrier to such a claim.
You should ensure that you could make a genuine business case for why the person was made redundant in the first place and what has changed now to allow you to re-advertise for that position.