I have always done this journey alone. Well, me and my two dogs. I enjoy the tranquility but unfortunately I only get to do this journey in the off-season, which is after September and before May. I am either going to work in Alaska, or coming south to visit family in the winter, so I always end up doing this drive outside of the "tourist season".
In the "off-season" a lot of places along the way are closed such as campgrounds/RV parks, museums, gas stations, etc., especially the farther north you get. I'm also usually in a hurry anyway, either rushing to get to work, or trying to outrun old man winter, so I rarely have time to dwell along the way. It's probably a blessing that most things to see are closed for the winter otherwise I'd be stopping all the time to look at different things and it would take a month of Sundays to make the journey. As it is, it takes me six days and I do make a point to change up the route a little every time, plus I try to stop to see at least one attraction. Last fall
I made a little detour through British Columbia to visit the West Coast Railway Museum in Squamish. That was well worth the detour.
During the summer season gas stations are pretty easy to come by, even up north. But when I make the journey, many of the ones in the smaller towns are boarded up for the winter. I only get about 10 to 12 miles per gallon towing and my stock 24 gallon tank didn't provide the range I needed for some stretches, so I had a high capacity (46 gallon) replacement fuel tank installed in my Tundra so I don't have to carry much extra gas. I still carry one 5 gallon jug though.
All I can recommend about buying gas is to try to do it in the larger towns where it's significantly cheaper, and when you are down to a 1/2 tank, start looking for gas.
One campground/RV park I've driven by many times and always wanted to stop at is near the White River in the Yukon. It's always closed when I drive by but if I ever get to do this drive at some other time of year, I would definitely be stopping here.
Discovery Yukon Lodgings: Cabins, RV and Tents
If you have any specific questions, post them here and I'll try to provide a useful response. But I'm getting ready to hit the road myself, probably leaving Southern California on Sunday, so I may be off-line for awhile after I depart.