sleeping thru the night

I have question for everyone. I have a two month old little girl. She was born a month early. I have been told by her pediatrician and lactation specialist to not let her go past four hours for eating. I feed her every three hours during the day or on demand and every four hours at night. I always have to wake her up for her nightly feedings. If I let her she would sleep the whole night. Question is should I let her sleep and she'll wake up when she's hungry or continue to get her up every four hours to eat?