It's highly unlikely she is anything but maybe 1 or maybe tops 2 months along. This would put you with due dates of late January through March. She likely has some milk left from being dried before her sale at the auction. This is also likely her son, if he is tame he was bottlefed and she doesn't even know it is her son, if he is wild, than perhaps it is he son with her dry now, she wants nothing to do with him. Has he tried to nurse her?
Take a good strong flashlight and see if you can see tattoo's in her ear

A herd of Alpines was just dispersed in your area, perhaps some went through the sale!
I would just let them be. A doe will put a younger buck into his place, and what to us is fighting to them is simple dominance, and putting each other in their place. Nobody wants to be alone during the winter without someone to cuddle up to!
Pay particular attention to your minerals, have them out clean and fresh in the barn. You live where copper is a huge issue, also Bo-se. You will want your PPM of copper up in the 1000's or higher, you may need to bolus, and to give Bo-se shots about 3 weeks before your doe is due (a perscription).
ADGA.org has clubs listed by state, may want to join one, they are a invaluable souce of information, finding a vet, newletters, and folks who love goats and love to talk goats! Nothing is better than learning about goats from folks in your area. Sannendoah.com is a wealth of information, read her copper information.
Get back to me if you find tattoo's in the ear, I am dying to know! The right ear will be the info of who the breeder is, the left we could probably figure out exactly how old your goats are. Vicki