The scale for Q Gauge is 1/4" to the foot, or O Scale. The proper scale for our 1 1/4" track gauge is 17/64" to the foot. That scale is not properly referred to as Q Scale, because it would conflict with Q Gauge, and cause unnecessary confusion.
I have been modeling in 17/64 scale for almost a half century. I probably qualify as an expert in this rather useless area of arcania.