Had a quick look to see who is responsible for pest control, I think it's the landlord and not the tenant .
The Standard Residential Tenancy Terms say that tenants must keep the place clean and not damage the premises (clause 63). If you follow your responsibilities under the Act and don’t cause an infestation of pests, then the landlord will be responsible for pest control as part of their responsibility to maintain the premises.
Tenants' Checklist