If you have Netflix (or access to someone elses) look up "Thumbs Up". It is basically a couple of guys who hitchhike around the US and document it. They do get a private plane (like a tiny prop plane) up to alaska. They meet some real weirdos and some other amazing folks along the way.
If you come through Chicago let me know. I should have heated floors by then
It can be brutal here in the winter and I do not even want to imagine what it would be like in Alaska at that same time of year. I would avoid it.
Also it seems like you are planning to travel through Canada (maybe) and bring a dog? Make sure to check into all the requirements and what not of traveling with an animal into Canada from the US. The borders are way more strict than they were years ago. I know you will need documentation of vaccinations and the like.
Anyhow be safe and enjoy your adventure!