As what as a cricket?
This sounds like a reference to the illustrated children's book by Audrey Wood. The title is I'm As Quick As A Cricket. Here it is on Amazon:
The phrase "quick as a cricket" was almost certainly created for this book. It is not a common expression in English otherwise. All the occurrences of this expression in Google seem to be references to the book. If it were a standard expression in English, it would appear in some ordinary context and not just in reference to children's literature.
The word cricket is a common noun; a word for any insect cricket or any game of cricket. A proper noun is the name of a specific person, place, thing, or a title; for example: Jiminy Cricket (from Pinocchio) Cricket Knoll, Wethersfield, CT or Cricket Street, Brisbane QLD, Australia JSCA International Cricket Stadium, Ranchi, Jharkhand, India International Cricket Council (ICC), Dubai, UAE "Cricket: Secret Child of a Sixties Supermodel" by Susan Fedorko