Synonyms for Carefree (same or very similar meaning)
WordNet sense 1 (free of trouble and worry and care):
unworried
WordNet sense 2 (not beset by troubles or disturbance or distress):
untroubled
WordNet sense 3 (cheerfully irresponsible):
devil-may-care, freewheeling, happy-go-lucky, harum-scarum, slaphappy
From the ODE community, based on WordNet
add/edit