From Longman Dictionary of Contemporary Englishdream something ↔ away phrasal verbWASTE somethingto waste time by thinking about what may happen She would just sit in her room dreaming away the hours. → dream→ See Verb table
Examples from the Corpus
dream away• Even now, 100 days before the start of the Centennial Olympics in Atlanta, the dream seems far away.• I watch the horrible dream drive away and disappear in a dribble of tail-lights.• The dream squelched away as she went ankle-deep into a pool.• But now most of the dragons slumber, dreaming the centuries away until the end of the world. 