Liverpool snapped up the young winger from Celtic last year and he has already made six senior appearances for the Reds despite being only 17.
Steve Clarke has already indicated that Doak, who is a regular in the Scotland Under-21s, could be called up to the senior national squad sooner than expected.
The teenager is considered a big talent in Scotland and Moore has conceded that he has not seen a quicker player than Doak in recent years.
The former Newcastle United star also stressed that Liverpool are the perfect setting for him to develop as they will allow him to play the kind of football that will get the best out of him.
Moore said on the Go Radio Football Show: “He is at the right club.
“He is just that wide player that can play and wants to get at people.
“He needs to be at a club that allows that kind of scenario to happen.
“He is at the perfect club and tell you what, I have not seen anything quicker in recent times.
“He is an absolute flying machine.”
Doak has featured four times for the Scotland Under-21s and is likely to be fast-tracked to the senior squad soon.