J.H.
Like you said every child is different, but I wouldn't try and keep her awake if she is tired. I would maybe try and give her some rice cereal with her last feeding. That made my daughter sleep longer through the night, but if she goes to bed at 8 and sleeps until 4 or 5 a.m. thats a pretty good streach, I'd consider that sleeping all night for her, although I know for you getting up at that time still seems like the middle of the night, ha, but I feel soon she'll sleep a little longer.