Mould can be a difficult issue.  Unfortunately you will find at various times, most houses will have environmental mould just because of the we weather we experience.

An owner is responsible for meeting the minimum housing standards which requires you to provide a property that is free from damp & mould, (but this does not include where the damp or mould has been caused but the tenant).  You also have to ensure the property has adequate plumbing and drainage.  

So it is possible for a tenant to argue that the mould is caused from damp due to a drainage issue or a leak.  I would recommend the property owner has a plumber check for leaks and drainage issues (roof leaks, pipe leaks, shower leaks, blocked downpipes, gutters or ground drains etc.)

If no leaks are found, you the owner needs to make sure there is no other structural issues that could be contributing to moisture in the property: vegetation too close to the house, are all of the windows working correctly and can be opened in all weather to ensure ventilation is maximised, etc.  

Any leaks or structural issues, would be considered emergency or urgent maintenance that needs to be undertaken at owner cost.  Clean up of the resultant mould would also be an owner cost.

If no leaks and no other structural cause for increased damp are found, then it is likely the cause is either enviromental (ie just because of high humidity due to the sheer amount of rainfall and lack of sunlight over an extended period of time), which unfortunately is unavoidable, or caused because the tenant is not ventilating as much as they should/could.  You need to investigate...
  • Do they keep windows open all year round?  
  • Are they using the exhaust fan/rangehoods every time they shower/cook (they should be left on for half an hour after using the stove or showering to make sure the air dries out)?  
  • Are exhaust fans/rangehoods/air conditioner filters clean (they won't work as efficiently as they can if they are dirty)?  
  • Are they using the dry setting on the air conditioner as this will help to dry the air?  
If the answer to any of these is NO, the tenant's actions/inactions are at the very least contributing to the mould, potentially though, if no source of the mould is found, they are causing the mould through their actions/inactions.

Both humidity related issues and a lack of use of the provided ventilation items would make the cleaning of the mould a tenant responsibilty.

Unfortunately there is no hard and fast rule.  You really need to eliminate causes and see what is left and it may be that it is a combination of causes and that may mean it is a joint responsibility between tenant and owner to resolve.

Below is a link to the minimum housing standards page on the RTA website.  It has some specific information regarding mould in the FAQ section.  

https://www.rta.qld.gov.au/during-a-tenancy/maintenance-and-repairs/minimum-housing-standards

I have also attached the mould fact sheet that we provide to tenants.  It has information about what causes mould, how to minimise/prevent environmental mould, and how best to remove it and clean it when needed.