I suggest getting familiar with the options of where you want to go, but leave the when flexible.
That way you can adapt for weather conditions or a temporary road closure without getting too stressed. For instance, when we get to Tok AK, I check the weather in Valdez. If it is a sunny forecast that is the direction we head first. Valdez in the rain isn't all that pleasant, yet in the sun it is lovely.
On occasion the Taylor Highway closes due to washouts. A few summers ago it was closed for a couple of months while repairs took place. Taylor/Top of the World aren't the most pleasant to drive when wet, so try to choose the better weather for it. We like it in September; generally drier and spectacular fall colours.
While you're up here, check the road reports now and then, or ask at the Tourist Info Centres. And adjust to suit. There usually aren't detours if something does go wrong and a road closes.
I'm not trying to scare you ... just want you to be aware of possibilities.