1812, "full of dots," from dot (n.) + -y (2). Meaning "silly" is from c. 1400, in dotypolle "dotty poll" (i.e. "dotty head"), in which case the first element is from dote (v.).
they are dotty about each other
dot
dotage
dotard
dote
doth
dotty
Douai
double
double agent
double date
Double Dutch