We are living in West Coast USA and are moving to Asia. Our dog has a severe emotional issue because he was a rescue from the streets. He is unable to be kenneled without massive panic attacks, anxiety, mania. So, he cannot fly. We are looking for options to bring him to Asia on ship or small charter plane where he could be with us in the cabin. Any thoughts? Thank you so much!
As per this post chartering a plane as an example from San Diego to Hawaii starts from $65000. That's about half way across but chartering a large enough plane to cross without refueling in Hawaii is going to be even more expensive. In conclusion, I have severe doubts private jet is doable below $100000.
OP asked whether there is a way to charter from Alaska into Siberia. The answer is yes, Bering Air flies from Nome to Ugolny (Anadyr). This is a short flight, even for a small aircraft this will take less than an hour. From there, I would probably fly into Sokol (922 miles) and next day to Ignatyevo (Blagoveshchensk) (1122 miles). The latter distance will determine which plane can you charter unless you want to refuel which will make a daunting long, long journey even worse. Some small piston planes can even do the Ugolny-Ignatyevo flight in one go (2041 miles) -- expect that to take like seven hours.
Ignatyevo airport serves the "metropolis" called Blagoveshchensk which has a ferry into Heihe, China. You can then take the train to Harbin, then another to Beijing and then the Z5 direct train to Hanoi (this alone is 36 hours). Phew!