I would bug out for Australia, by air if possible from Alaska, if not by boat.
Actually I kinda wonder if Alaska would see much of any severe effects.
Unlikely. At least for a while. Warmer pacific currents keep the coastal regions relatively temperate in the south, and those would not see effects until the oceans cooled. Prevailing winds would shift slightly toward the hot spot that the eruption would maintain, but I think the general effects would not be immediate. It might be hard to book passage or get a flight, though.
As for me, moving west or south would take me into the thick of things--I'd be stuck with a more northerly and eastward route.