Falling asleep while breastfeeding

So lately, especially during night feedings, I fall asleep while feeding my baby girl.  My husband also falls asleep so the three of us end up sleeping.  I never wanted to co-sleep for safety reasons and just personally I want her to use her own sleeping area but since I keep falling asleep this hasn't been happening.  She's 9 days old and if we move her to bassinet almost immediately she wakes up, cries till I feed her again and falls asleep on/next to me.  And repeat.  Am I doomed now cause it seems she will only sleep if she remains next to me, sigh.  I don't want her to get hurt and I don't want her to become dependent on me being there to sleep... What can I do?  Anyone with similar prob?  I try keeping myself awake but no matter what I do, I end up sleeping.