I am buying my first home with FHOG in NSW, tenants leave in Oct, can I write losses in tax before I move in?

FHOG = First Home Owner Grant. As it won't be vacant until October until the lease expires, as I am getting the grant and it is not an investment property can I still claim interest and other costs until we move in?

To be eligible for the grant you must move into the property for 6 months of the first 12 months of ownership. Therefore you are well within your rights to rent the property for six months before moving into it. If you adhere to these rules, then yes you can claim your rental losses on your tax and still qualify for the grant, I did the same thing myself.

You can claim such expenses as are applicable to any rental property. However, I would doubt that any significant repairs would be allowable unless you can show they are specifically relative to tenancy.
You would be limited to expenses only applicable to that period in which you have tenants. Any period in which there are no tenants would not be allowable as the property is not being 'held' as an investment.

If you are getting the grant then you are treating it as your Principal residence. If you decide to claim interest and other costs you would have to have income against this i.e. rental income and therefore it would be an investment property.
Either way, if you are receiving the FHOG you will lose the grant if you do not live in the house within 12 months after purchase and for an occupying period of at least 6 months.

I would be inclined to ask a tax accountant