I assumed it meant to the outer reaches of this galaxy, which would fit.
There is no reason why "vernal" would mean that. It literally means "pertaining to spring," or can figuratively mean youthful or new. It would be oddly poetic and metaphorical to use it as a synonym for "uncharted"; one would think that official military orders would require more clarity.
Bottom line, most laypeople don't understand what "galaxy" means, and TV writers are generally no exception. Lots of TV shows and movies have had spaceships traveling casually between "galaxies" without any regard to whether it made astronomical sense. The original Battlestar Galactica
had the fleet traveling through several galaxies in the course of a year -- at sublight speeds
. The "Vernal Galaxy" thing was a goof, like so very, very many other SFTV goofs.