Old English carleasnes "freedom from anxiety;" see careless + -ness. The original sense is obsolete. The meaning "heedlessness, negligence" (1560s) probably is a fresh formation.
Entries linking to carelessness
careless adj.
Old English carleas "free from anxiety; unconcerned," from care (n.) + -less; a compound probably from Proto-Germanic (compare Old Norse kærulauss "quit, free"). The original recorded senses was extinct by mid-17c. (now in care-free); the main modern meaning "not paying attention, inattentive, not taking due care" is attested by 1560s (in carelessly). The meaning "done or said without care, unconsidered" is from 1650s.
-ness
word-forming element denoting action, quality, or state, attached to an adjective or past participle to form an abstract noun, from Old English -nes(s), from Proto-Germanic *in-assu- (cognates: Old Saxon -nissi, Middle Dutch -nisse, Dutch -nis, Old High German -nissa, German -nis, Gothic -inassus), from *-in-, originally belonging to the noun stem, + *-assu-, abstract noun suffix, probably from the same root as Latin -tudo (see -tude).