double time vs double quick

double time is a noun but double quick is not a noun.

Word	Noun	Adjective	Verb	Adverb
double time	Yes	No	No	Yes
double quick	No	No	No	Yes

As adverbs, double time and double quick are synonyms defined as:

double time (noun)	double quick (noun)
a doubled wage (for working overtime)
a fast marching pace (180 steps/min) or slow jog

double time (adverb)	double quick (adverb)
at a faster speed	at a faster speed