An EQUINE layout sounds like taking Dvorak to an extreme. E is the most common letter in English? Let's give the keyboard two of them! I'm half-tempted to mock up up such a layout just for giggles. It'd be a handy layout for dolphin.town, especially.
I'm running this to its ridiculous extreme. I'm imagining a keyboard layout that has duplicate keys matching letter frequency. The keyboard has to have 56 Es just to be allowed a Q. About 35 or so Ts. Etc.
The odds favor you getting the key you want, so it's best to not even look.
That could certainly put a Quine in EQUINE. Mash the keyboard all at once to get a frequency chart that resembles the keyboard. That's your new keyboard.