Sleep question from paranoid new Mom!?

My baby girl was 5 weeks early and weighed 5lbs11oz. We fed her every 3 hours (start to start) because she was a bit small but now the doctor doesn't seem too concerned about the strict eating schedule, at 9 weeks she is now 9lbs4oz! My question is about night time feedings. She has a bottle at about 9:30pm and then she sleeps until about 5am unless I wake her. If I do wake her it takes 2 hours to get her to settle again and so my mom says I should just let her sleep as she will cry if she's hungry. Is this okay? I have let her sleep twice now and she ends up drinking larger bottles in the day to make up for it so she is getting the same amount of formula in a 24hr period. I am just worried that 7-8hours between feedings is too long? Thanks for your opinions....I must admit the sleep is nice but my baby's health comes first! :)