My experience is that AS is very generous with award seats, but then again it is high season in Alaska and it is late in the game for planning, so who knows what availability is like (Barrow is a VERY popular destination around solstice time).
If AS is flying a 737 combi, then there is no F class. PenAir is available for award seats but I believe only between ANC and a couple of destinations in SW AK.
More answers can be obtained from alaskaair.com. I believe their own award rules and availability will mirror what you can get using Qantas miles.