I’ve never specifically hunted Sheep or Goats, but I have never heard the phrase “bagging a nanny” before. I would comment that I assume it is not a permeating phrase, but possibly an individual or regional colloquialism. I’d also suggest its use by someone on the outside looking in will sound disingenuous and inauthentic, so I wouldn’t personally adopt the phrase. Coming off as falsely representing yourself by forcing an unnatural phrase across your tongue is a great way to ruin interest from those hunters with actual experience. Really can’t sound smarter or more experienced than you really are without being obviously deceitful.
I’m not a huge fan of the now-old-world term “bagging” in general, so this wouldn’t be integral to my vernacular even if I DID commonly hunt sheep (which aren’t “nanny” anyway) or goats, even females.