Am I under-gunned without a 12ga for home defense?
No.
You are the weapon, the world is your toolbox.
Access your environment, and do so from the perspective, you are a criminal, and how would take yourself down.
What areas of property, and home, make it easy to take yourself down, and which areas make it difficult?
MY concerns, have always been, entering, exiting, a structure, and answering the door. The handgun fits these needs, quite well, and most often better than a long gun.
Note: One suggestion, a strong one, is to have home guns, that the smallest person that might have to employ, can do so effectively.
"Small" is not meant in a derogatory fashion.
This not only refers to physical size, also age strength, any physical limits, experience, etc.
Keep in mind, YOU could have an accident, or be ill, or recovering from surgery, and in this context be "smaller" than you presently are now.
So, while a 12 ga is a good choice, some find a 20 ga to work best for their home /property needs.
Others may find a .30cal M1 carbine, Ruger Mini 14, or one of the AR platforms best.
While even others find a Lever action rifle in .357 works best.
Remember, none of us are going to be with you, and yours, when matters go rodeo.
So while we share experience, strength and hope, YOU still have to access, investigate, and verify what works best for you.
steve