It is not correct for your cousin to apply for both types of credit, as this could put her into debt.
We can arrive at this answer because:
Your cousin's available funds are too little to guarantee both types of credit.
That's because they would demand a lot of money and leave her with few resources to meet her needs.
In this case, it would be more important for your cousin to save money, in investments that yield profits, such as savings cards, shares, real estate credits, among others that would allow her to have enough money ina period to buy a car.
While she capitalizes on these investments, she must apply the credit card application, which should only be used in emergency cases, to help her save money.
About the need to buy a car, your cousin can buy a used and cheaper car, for as long as she doesn't have enough money to buy the car she wants.