I’ve long thought that Carroll’s beast contributed to the development of the sense, but the OED2 derives the adjective from the verb snark (to snore or snort; to find fault with or nag) and not from the noun (Carroll’s use).
If you get so snarky with someone that they softly and silently vanish away, have you been boojumy?
narked = irritated, put out. From the verb nark, to annoy or exasperate.
Curiously, “nark” meant “a police informer” or “to act as an informer” all the way back in the mid-1800s, apparently quite unrelated to narcotics enforcement.