Have you tried nursing her as soon as she wakes up? If she's been asleep already, maybe she'll be more likely to stay awake to eat, rather than fall asleep after 3-5 mins of nursing? Something to try if you aren't already on a sleep - eat- play schedule.
Also for peace of mind, my DD weighed 8 lbs 1.5 oz at birth, and I just checked the back of her drs appt cards and she STILL wasn't back up to BW at her 4 week check up (she weighed in at 8 lbs .5 oz). She's now 2.5 and doing fine. You'll figure it out!