1651, said to have been applied to them in 1650 by Justice Bennett at Derby, from George Fox's admonition to his followers to "tremble at the Word of the Lord;" but the word was used earlier of foreign sects given to fits of shaking during religious fervor, and that is likely the source here. Either way, it never was an official name of the Religious Society of Friends. The word in a literal sense is attested from early 15c., an agent noun from quake (v.).
Quaker gun (1809, American English) was a log painted black and propped up to look from a distance like a cannon, so called for the sect's noted pacifism. Philadelphia, Pennsylvania, has been known as the Quaker City since at least 1824. Related: Quakerish; Quakeress ("a female Quaker"); Quakerism