In Australia you can even take your car back after the purchase. I am going to look that up.... here it is.
Under the Australian Consumer Law, when you buy products and services they come with automatic guarantees that they will work and do what you asked for. If you buy something that isn't right, you have consumer rights.
Also, check this. Lemon laws protect you- Car News | CarsGuide
When you buy a car from a dealer, you now have the protection of legally enforceable consumer guarantees, including that the car is of acceptable quality (which includes being safe, free from defects and durable) and reasonably fit for any purpose you specify when buying it, such as towing.
If you have what the ACL calls a major failure with your car, you are entitled to return it to the dealer to claim a refund, or a replacement -- your choice of an identical new car or one of similar value.
A major failure is when a reasonable consumer would not have bought the car if they had known about the problem, or when the car is substantially unfit for its normal purpose.
In other words -- the car is a lemon.