Being in the Uinted States on a K1 Visa is different than being here as a Permanent Resident or Citizen.
travel.state.gov
If you have completed your marriage (civil paperwork), your new wife should transition from her K1 Visa.
Overview: What Is a K-1 Visa?
The fiancé(e) K-1 nonimmigrant visa is for the foreign-citizen fiancé(e) of a United States (U.S.) citizen. The K-1 visa permits the foreign-citizen fiancé(e) to travel to the United States and marry his or her U.S. citizen sponsor within 90 days of arrival. The foreign-citizen will then apply for adjustment of status to a permanent resident (LPR) with the Department of Homeland Security (DHS), U.S. Citizenship and Immigration Services (USCIS). Because a fiancé(e) visa permits the holder to immigrate to the U.S. and marry a U.S. citizen shortly after arrival in the United States, the fiancé(e) must meet some of the requirements of an immigrant visa.
After your marriage, you should be applying for a Permanent Resident (Green Card) status.
Once you have the permanent resident status, you most likely comply with West Virginia's requirements for permitless concealed carry as well as legal requirements for firearms possession.
It may not be legally possible for you to transfer a handgun to her until she has reached this status either. You have to be careful to avoid straw purchase laws as well in which you fill out a 4473 as if buying the gun for yourself, and then immediately transfer the firearm to someone else. Some states also require transfer of a handgun formally through a FFL, or via a purchase permit, It would be best to check on West Virginia law to see if you have encountered any issues.
If you are working with a lawyer on making the transition from your wife's K1 to Green Card, I would recommend discussing all this with that attorney.