c. 1500, colloquial diminutive of dad, with -y (3). Slang daddy-o is attested by 1949, from bop talk.
Daddy-long-legs is from 1814 in Britain as "crane-fly," a slender, long-legged summer fly. In the U.S., it was used by 1865 as the word for a spider-like arachnid with a small round body and very long, slender legs.
A superstition obtains among our cow-boys that if a cow be lost, its whereabouts may be learned by inquiring of the Daddy-Long-legs (Phalangium), which points out the direction of the lost animal with one of its fore legs. [Frank Cowan, "Curious Facts in the History of Insects, Including Spiders and Scorpions," Philadelphia, 1865]