How do I help with my new (but 1 yr old) dog's separation anxiety?

I just got a 1 year old chihuahua/dachshund from a friend a few states away. He's remarkably well behaved considering a huge family and climate change, but he whines when he's alone (if I go to the bathroom), strews clothes if we leave, and gnaws on his feet all the time (no fleas or other visible/tactile damage or issue). I know what to do to train him (calm routines for leaving, radio, Kong toy, etc.) but I need advice for the immediate future. Please and thank you.