GG: «Boy, the sound sounds like a cat purring, but that's not right, becuase you said it's the base form, which is purr.»
The action denoted by my verb is often accompanied by purring. And yes, the agent is a cat!
As to whether my term applies only to domestic animals (namely pet cats) — I am not %100 sure, but you may be certain that it is so in the majoroty of cases.
(EDIT: I mean I did mean pet cats when proposing this verb)