My 2 cents...
(Disclaimer: I always offer more information than people ask for. My wife tells me it is an illness

)
You have two routes to choose from leaving from Toronto...
401, I-75 (crossing the border at Windsor or Sarnia): Driving time @ 25 hours. Most people take this route in the bad winter months as you stay on I-75 all the way and there are more exits for hotels/restaurants etc...Also, the mountainous area is more brief so it is believed you'll encounter less inclement weather. Those with young families often suggest this route as there is more for kids to see while driving and more places to pull off and experience.
QEW, I-190, I-90, I-79, US19, I-77, I-26, I-95, I-4 (crossing the border at Lewiston or Fort Erie): Driving time @ 22 hours. If the weather looks like it will be fine then this is a quicker and more scenic route.
Timing the mountains on the second route...
The mountains are mainly in W.VA and VA. While you begin heading into the mountains as soon as you hit Morgantown your real ascent into the mountains begins at the US19 (1000ft elevation). By the time you get to Beckley you're at a 2300ft elevation. At Bluefields (this is where the two big tunnels through the mountains are) you're at about a 2500ft elevation and by the NC border you're down to about a 1300ft elevation. It's the drive between Beckley and the NC border where you notice the mountains the most.
We live in Burlington at the QEW. It takes us 7.75 hours to the US19...8.75 hours to Beckley...10.75 hours to the NC welcome center. We cross the US border when there's no traffic. We stop twice before the NC border...once for lunch/gas and once for gas only. We don't have kids...
If you leave from Toronto, presuming you cross the US border when it isn't busy and presuming you make minimal stops along the way, I'd expect you to be in the main mountains between the 8.5 hour mark and the 11.5 hour mark.
Enjoy your trip