Ah, riding up to Alaska to start a summer job after uni, classic trip.
There's lots of folks migrating up at that time of year. By bike, the biggest issue will be the weather. It's early spring so it can be cold and rainy. It also can be fine some days, but I would plan for some wet weather.
Your projected distance per day is certainly doable as the highways are great and the further north you go the less traffic there is. However you will have to maintain a steady pace as you are riding fairly good mileage everyday. Mid summer, not a problem but in early spring if it's wet and you are getting cold, you end up stopping a lot to warm up.
You didn't mention what type of bike you are riding but whatever you ride, make sure you have very good rain gear.
In regards to route, it's fine. You can make it more scenic by riding through or near the Rockies once you hit Calgary and also in the southern part of the province, but you live in the mountains already and have limited time so you may want to save the meandering for you return trip.
No special documents other than registration in your name and a passport.
Have a great ride and take plenty of pictures. It will no doubt be a memorable summer and one you will look back on fondly for many years in the future.