I don't know that there are more per capita doses, but the doses that are here are being given out very quickly. That is because of two factors:
1. The vaccine is being distributed and administered by multiple agencies. The Alaska Native Health Service, the Veteran's Administration, the military and the by the state through hospitals, clinics, et c. A good buddy of mine who is Eskimo, with no health risks, is not a senior citizen, et c. has already received the first dose of a vaccine. (I'm glad he was able to, but I'm envious that I can't yet.)
2. The sites that were prepared for patient overflow have been repurposed now for vaccines. These are large sites (relative to our small population) that can handle significant traffic.
All of that said, there are also attitude differences that work in Alaska's favor, and a relatively small population to organize for. Besides, last summer was lost to much of the population. Summers are very important, and nobody wants to lose another. (Lots of space mitigates it, but there are still lots of social activities.)