What kind of photographer are you? I don't own a Nikon V1, but from what I've read it has definite strengths that far exceed the Q, which may be of interest to you depending what sort of pictures you take. It excels at high speed photography. On the other hand, I've read that access to manual controls is discouraged by the control and menu setup. In that way it seems to be a very souped up point and shoot -- change the picture mode dial and let the camera decide. As others have pointed out, the Q handles much like a miniaturized Pentax DSLR.
Another consideration, what kind of lenses does the Nikon have vs the Q? To me, the fisheye lens is terrific, despite being designated as a toy lens. How important is size for you? The Q is very small.
If you end up getting more lenses for your K-01, then, as post_eos points out, the crop engine/magnification of the small sensor could take you interesting places with an adapter for the Q, if you don't mind manual focus.
Originally posted by Amaroq Recently picked up a k-01. Love it! Thinking of adding a Q but I've gone back and forth a few times between it and a nikon v1. I know a few k-01'ers have a Q too, and am curious if you find the Q adds something unique or worthwhile to your kit.