This is general coverage of this topic - you should seek advice from an employment law specialist or TAPS to ensure that the termination payment is set up and processed correctly.
In general, termination payments (other than unused leave) are classified depending on the nature of the payment (e.g. Pay in lieu of notice is treated differently to a Redundancy payment) - SmoothPay provides for all known ATO classifications and taxes accordingly (it also provides the foundation rules for superannuation and how the payment will appear on the employee's Payment Summary - use the [info] tool beside each allowance code to see these definitions).
Note too that some payments are "Age-dependant", thus payments made to a person under 55 years of age may be taxed differently to payments made to person over that age (which is why we advise you to obtain correct legal advice).
If you don't have a suitable allowance code established for the type of payment you wish to make then add a new allowance code (Codes..Allowances..[+]) and edit to suit. Pay particular attention to the Category (there are separate sections for Resignations or Dismissals and Genuine Redundancies - the distinctions are important from a tax point of view and affect how the payment appears on the employee's Payment Summary.
Please make sure you check your employee's award or Enterprise Agreement for any and all termination provisions.