Your employer should not come running to you for the reimbursement of repair costs which the dealer claims are not covered under warranty. Where the dealer has provided the car with a warranty against defects the dealer must comply with the terms of this warranty.
Even if the defect is not claimable under the warranty, there are further protections under the Australian Consumer Law that apply to new and used vehicles sold to a consumer. This includes a guarantee that the car be fit for purpose and of an acceptable quality.