Besides a generator, you need to look at your power converter/battery charger. The basic ones take a LONG (like 12+hours) time to recharge your house batteries. Fine if you are driving every day or hooked up to shore power at night, but inadequate for generator charging.
Chances are you will not use air conditioning up here. It really doesn't get dark, so you don't use your interior lights very much. In places you'd like to boondock, invariably there's no TV reception, so you can probably cross that AC load off the list as well. Can you get by using your gas stove instead of the microwave while boondocking? If so, you might be able to meet your needs with just a small inverter.
FYI, places like Denali NP have limited hours you are allowed to run your generator (which often coincide with when you'd want to be taking the bus further into the park).
So, I'm not so sure I'd suggest running out and buying a generator just for this trip. FWIW, I added a few additional house batteries to my class C, and installed a high-performance charger/inverter. We rarely run the generator for any length of time.