1940s. Apparently from antsy (although this is first attested slightly later) + pants + -y (as a rhyming pair), probably after to have ants in one's pants.
Definition of antsy-pantsy in US English:
antsy-pantsy
adjectiveˌan(t)siˈpan(t)si
US informal
Antsy. Compare to have ants in one's pants.
Origin
1940s. Apparently from antsy (although this is first attested slightly later) + pants + -y (as a rhyming pair), probably after to have ants in one's pants.