My daughter seriously slept and ate for the first month of her life. I was told that (while breastfeeding) once she get back up to her birth weight that it was fine to let her sleep and feed her on demand. I never woke her up... she would wake up when she was hungry and usually nurse back to sleep. I am not kidding when I say that she would wake up, eat and go back to sleep... She was probably about two months old before she would stay awake for a significant amount of time, but I was told not to worry and not to wake her up. Now... she never wants to go to sleep, lol, she wants to play and mess around with her brother, she just turned 2... it's sad how time flies
Babies will wake when they are hungry. As long as your LO is putting on weight then it is fine. She should be having plenty of wet nappies which indicates she is getting enough fluid into her system. Babies will often have one long sleep period at night that should get longer as they get older. My second son used to sleep for four hours at night at about five weeks.