The message .com
from "Irene" contains these words:

I believe my rosa rugosa has self-seeded. Or is it possible to have a
runner?

Both are possible , but runners/suckers are much more common.

I've got what appears to be a new shoot about a foot away from
my existing rosa rugosa.

That sounds like a runner/sucker. R rugosa are not usually grafted, so
the root sucker will match the parent.

My question is - how long should I wait before I move it somewhere
else? Right now, it's about 8" tall. I can't leave it where it is for
very long, since it is in between two rose bushes.

Rugosa leaves are already in growth so moving is a bit late for this
season, autumn would be better. However, what most people do with rugosa
each year is to prune out some of the oldest stems right to the ground,
leaving the suckers as replacements.

Janet