Hi M.,
Not sure where you had you baby, but most local hospitals will tell you exactly how much milk your baby is getting if you go in for post partum nursing clinic. Now then, for your sleepy little girl...your milk has probably just come in a couple of days ago so she will be getting the nutrition she needs. Try one of a couple of thing: 1) Nurse on one side for a few minutes, then try to burp and switch sides. 2) Uncover her, change her diaper first etc. 3) To make certain she is getting the hind milk which is higher in fat, nurse on one side only per time, BUT then you have to pump on the other side so that you keep your supply up. Chances are if she if falling asleep before that happen though keep her uncovered, tap her feet to wake her, try "chicken arms" to awaken her, pull her off, set her up, burp her etc. As she gets a little older she will stay awake longer. Lastly, try to offer your breast every 2 or 3 hours during the day and no longer than 4 to 5 hours at night. She may only suck a small bit, but she will still be getting some. Make sure you are getting enough water when you are nursing too to keep her well hydrated. Congratulations on your decision to nurse you daughter, it is the best thing for her her!