L.C.
Hi T.,
At 2 years old a small pillow is probably ok. They are more concerned with infants having pillows because they can suffocate. A 2 year old can lift her head or roll over if the pillow is on her face. (And she can throw it at you!) I bought my son a really small pillow - about the size of an airplane pillow when he was 2.
Have you asked your daughter if she wants a pillow? She may say no and just want to sleep with her blanket as a pillow.
Good luck!