for safety sake you shoudl always Df out of the cot.
just gently lift her out and sit in a chair in very dim to dark room and feed quietly with no talking or eye contact. don't change her unless her nappy is soaked through to her bedding or she poops.
if you are Bf for Df Tracy recommends "before you give him your breast, stroke his bottom lip with your pinky or a dummy to get his sucking reflex started. Either way, at the end of the dream feed, your baby will be so relaxed you can put him down without burping"
if baby wakes when you go to do Df do not stress about it - most likely she will drift back to sleep during DF and that is fine. f baby won't take the feed, try again in 15-20 min to catch at a different point in her sleep cycle - she may just be in too deep a sleep.