We are 55' and we fit in the spots we stay in. You are looking at around 71'. So yes, it would limit you. And I think you are right, with limited time the side excursions will be few. Most of the "attractions" have space for motorhomes and trailers, but it may involve a bit of a walk.
As mentioned, we do this every year. I don't take spare parts. The foul weather gear is a medium weight all season jacket and a shell with hood. Trustworthy Hardware in Soldotna sells fit-for-purpose fishing gear at a reasonable price if salmon on the Kenai are your interest. Any guide or charter will furnish everything needed.
In Canada the roads will be good and the speed limits usually are 100Km/Hr and sometimes higher, until you pass Ft Nelson. Beyond there, there are places with construction, and places the road narrows until you cross the Liard River, then it is pretty good again until you pass Whitehorse. Pay attention to sue t.
So my suggestion is leave the trailer at home for this trip. It will be a hindrance for the whole trip and only useful for one of two days.
I hope you can take the time to post a summary of your trip when you are done. Have fun and enjoy it.