It sounds like the seat is installed a little too upright for a newborn. For a newborn/young baby, the seat should be at a 45 degree angle.
Also alot of times the newborn headrests do more harm than good, try removing it and using a rolled up receiving blanket on each side of her head (NEVER under her or around the harness) but just beside her. This will also support her body a little more too, as newborns tend to not fit as well even in infant seats if they are very small.
www.safekids.org and find a car seat event in your area. Make sure whoever installs your seat is a SAFE KIDS CERTIFIED CPST and not just a random person at hte fire department or police station. Most of the time police officers and fireman have had only a 2hr training one time, but CPST's are trained yearly and continually on best practice and new advice.
3 out of every 4 car seats is installed and used wrong, chances are yours is one of them. Get it checked by a CPST to make sure its in right and being used right 100% of the time.
Sometimes all it takes is just a tightly rolled up towel or cut up pool noodle under the base of the car seat (tucked into the bight of the vehicle seat) to recline the seat enough. Most new vehicles have very angled seats, so it makes the car seat install more upright than it should be.