Is the death of a paternal cousin's daughter resulting from a car accident considered murder, and what are the implications for the driver in this case?

If you have inspected the car and confirmed its roadworthiness, not violated traffic laws, and no negligence occurred on your part, then there is no blame on you, Islamically, for any resulting injuries or accidents.

However, if you neglected safety measures, then you owe expiation for accidental killing, which is the freeing of a believing slave. If you cannot find one, then it is fasting for two consecutive months, along with repentance to Allah, and the payment of blood money for the deceased by the 'Aqilah (male relatives on the father's side) unless the blood relatives pardon it. This is based on the Almighty's saying: "And never is it for a believer to kill a believer except by mistake. And whoever kills a believer by mistake – then liberaration of a believing slave and a compensation payment presented to his family, unless they give [it in] charity. But if he was from a people hostile to you and he was a believer, then liberation of a believing slave. And if he was from a people with whom you have a treaty – then a compensation payment presented to his family and liberation of a believing slave. And he who does not find [one] – then a fast for two consecutive months as repentance to Allah. And Allah is ever Knowing and Wise."

If your uncle pardons the blood money, it is waived for you if he is the sole heir. If there are others with him, only his share is waived.

As for if you dozed off (fell asleep) while driving: if you did not feel drowsy before that and it came upon you suddenly, then there is no blame on you. But if you felt drowsy before driving, then you owe blood money and expiation.