Hi there! I'm a lactation educator with A Mother's Haven in Encino and a breastfeeding mom too. My son didn't really start getting onto a schedule until he was between 4 and 5 months and he didn't sleep through the night until he 10 and a half months. Every baby is different.
As far as breastfeeding goes, at 1 month your grand daughter should be nursing every 1 1/2 to 3 hours. The length of each nursing really depends on what type of eater she is. Some babies are able to drain mom's breast in 10 minutes and don't want to nurse from the second breast until their next nursing session. My son nursed 15 to 20 minutes on each breast during each nursing session. Also something to keep in mind is that babies usually increase the number of times they nurse at 3 and 6 weeks when they have growth spurts. Because breastfeeding is demand and supply, it's their way of letting mom's body know it's time to produce more milk.
I would recommend continuing to nurse every 1 1/2 to 3 hours during the day yet, but if your grand daughter has been gaining weight well she could do on demand nursings at night. Mom can do a dream feed (like you did by waking your baby at 11pm) before mom goes to bed. She only has to wake the baby enough to get her to nurse, but that should help your grand daughter sleep a longer period at night. Instead of 3 hours she might go 5 or 6, depending on how much milk she takes in during the dream feed.
If you have any other questions or if Mom needs more help you can reach me here at through A Mother's Haven. They're number is ###-###-####. I hope it all works out and the new mom isn't too stressed!