Dakota
Veteran Expediter
No, you're right. The original of the modern word is expeditor, and is technically the correct spelling, although at this point both are equally correct and have identical definitions.
The word origin of "expedite" is from the Latin expedīre, which is literally to free (ex) the feet (ped) (from "fetter", as from a snare), hence, liberate, from ex- + pēs foot. The past participle of expedīre is expeditus.
The -or is a "Latin occupational suffix" (of expeditus), thus expeditor.
Because the -or expeditor sounds like the -er expediter when pronounced, the spelling naturally morphed into the -er expediter. This began to happen in the late 1890's when the term began to be used more and more within the scope of the Industrial Revolution. Most American English spell checkers will have the -er expediter listed, as it is the more common spelling for American English, and will show the alternate (original and technically correct) spelling as being incorrect.
Kinda like those wacky Canadians throwing a U around in certain words