At such a young age it is very common for your lo to fall asleep during a feed, and when you wake them up they have not actually finished the feed and are still wanting more.
When you see your lo starting to dose on a feed, I would try and wind her at this stage to try and wake her up - once she has been winded and is awake you can offer the feed again. Also massaging their feet or the palm of their hand can keep them awake.
If your lo does fall asleep at a feed, I would then change her nappy, wind her and then offer her the feed again, once she has taken what she wants you can do your few mintues of A time before going down for a nap.
Also do you offer a pacci / dummy? Quite a few babies need that sucking reflex, and will still root after a feed even though they are not hungry - a pacci may help with this and help her soothe herself to sleep.
HTH's
Paula