Pillow is not good for her neck at this age and it may also hinder her head movement. You never know, sometimes the bb may move their head and body at night and a pillow may cover the bb face and cause suffocation.
Most doctors and nurses do not suggest to use pillow for bb especially at this age. You should also keep the bb's bed as little things as possible. Don't put any toys or pillow around bb. My girl only has a light towel to cover her body during summer and a quilt during winter.
If you remember, when you bb was born, the hospital did not provide any pillow to your newborn bb as well.