I am still having trouble posting or replying to personal messages, so I am posting this topic in response to a private inquiry. Public or private, it holds my best advice. The style of writing may vary a bit, that is all.
There are a few things I will suggest, the first is to check weatherunderground.com and their "travel and activities" tab, going to Trip Planner. Road Trip Planner is also very handy when you are underway, but it only goes out one week from the day of inquiry.
On Trip Planner plug in the dates you expect to be somewhere, using a range of before and after dates if you wish. They will give you the historical records and calculated odds on what weather to expect. I am catching up on many things after an extended road trip myself, so I will leave it to you to experiment and try different dates or routes.
Carefully consider the second week in September weather reports, and check road sites as well for Alaska and the Yukon. It used to be you could count on the northern roads closing for the winter mid Sept to beginning of October, although this has changed radically as Alaska has warmed up. (global warming is subject to Political Science, but scientists and engineers are working with the facts that Alaska and the Arctic have warmed substantially and all we studied in the 1970's and 80's is no longer valid).
I made the trip from Alaska through Edmonton last May and did it as a stop-and-go tourist. It was great. This summer I plan on auto touring Alaska and the Yukon, but evidently earlier than you are planning on going. Yes, you will encounter fall colors, and as you go north you may pass through the brightest fall colors to the duller colors of late fall without the bright yellows. The road itself is well worth driving and I will do the trip to Whitehorse, north to Dawson, and then slowly back to Tok so I can enjoy the beauty. I will bypass the Mentasta Cutoff (Tok to Gulkanna) and go up to Delta Junction and down through Isabel pass (If I didn't go up that way to begin with). It is my old playground and I have a few places I have to check out in detail between Delta Jct. and Paxson. To me it is a truly spectacular part of Alaska, and I will go at the first sunny opportunity and perhaps the second sunny opportunity as well. It is worth skipping only if there are low clouds, rain or heavy forest fire smoke. Even in those cases, there is the chance it will be clear on the other side of the mountains.
Plan time so you can take a leisurely stop at Liard Hot Springs, you and the wife will like them. There is a lodge across the road, I believe (I camp).
Should give you plenty to explore.
In addition to weatherunderground.com I have used weather.com Seeing that it covers Canada whereas weatherunderground does not.
In summary, I would be cautious about Top of the World Highway in late September. Believe the weather forecasters and any warnings they or the road sites may offer you. One year I missed bringing a truck back from Central to Fairbanks by one week. I tried the road and the blowing storm and drifts at the mountain pass turned me around. I took 45 minutes to turn the truck around very, very carefully. It was no place to make a mistake.
For myself, if the weather is predicted to be good and there are no road warnings or closures, I would make the drive as you propose. The locals at that time will pay close attention and keep you out of trouble. Frommers says "The Top of the World Highway isn't maintained during winter; it's generally free of snow April through mid-October." so you should be just fine. Just check projected temperatures for that time of year to make sure they are in your comfort & desired zone.
Good luck and enjoy!