OK, you're headed to Quebec City. Quebec is the whole province -- Quebec City is... a city. I'm not trying to be nitpicky or critical, just letting you know that if you say "we're driving to Quebec," that's a big area and could mean a lot of different routes, so make sure you're specific if you need to ask for directions :-)
So from Woodstock you'll likely head up I-89 to the border. Along this route, you can stop in Waterbury and do the Ben & Jerry's factory tour, which is fun. There are also some good restaurants in the Waterbury area; it's had a growing "foodie" reputation over the last few years.
There are some shops and places to stop along Route 100 north of Waterbury, including the Cold Hollow Cider Mill and a Cabot cheese store. You’ll find Cabot everywhere; we are pretty serious about our dairy here — just ask someone for their opinion on the best cheddar or milk and you can get a very strong reply! Used to be a glass blowing studio with demonstrations along Rte 100 but I think he may have closed.
If Woodstock wasn't enough quaintness for you, you could head further up Route 100 to Stowe, which is lovely in the winter. If you have any winter gear with you (boots, especially), you can rent snowshoes and do some hiking, or you could rent equipment and go skiing (you can do this at multiple places along your route -- Stowe will be one of the most expensive).
If downhill skiing isn’t your thing (and even if you’ve never done it before, it’s easy to try — lessons/instructors are at every mountain, as well as bunny slopes and gear rental), then try cross country skiing. Very easy to pick up and a lovely way to spend some time outside. You can do this in many places in Vermont, just google.
In Stowe there is a nice bike path along the river, which will likely be either cleared or packed snow, so it will be easy for walking.
For a really “authentic” Vermont experience, stop at Cochran’s ski area in Richmond and take a lesson. It’s very small and very famous; many, many, many kids have learned to ski there, including lots of Olympic athletes. On Friday nights you can ski under the lights and have a sit down dinner, all for $10.
Burlington is a nice stop along the way, although the downtown area in recent years has really degraded. There are still good restaurants along Church Street and the waterfront and it is known for its many brew pubs. Check to see if there are any interesting shows at the Flynn Theater. But don't stray too far off of Church Street at night -- some areas are getting sketchy, very sadly.
Jay Peak Resort would be a nice overnight or two. It has an indoor water park and lots of outdoor activities.
Vermont is really about the outdoors, so, depending on the weather and what you have packed, see if you can get out and take some walks, go sledding, get outside.
And definitely plan some time in Montreal. There is a ton of stuff to do, just google for your interests.
Do pay attention to the weather. Roads are very well maintained in Vermont and drivers are generally cautious, but you have to be aware of changing conditions. The stretch of I-89 between exits 3 and 9 is especially prone to slippery road surfaces because of the elevation, and things can change fast. Slow down and don't be afraid to get off the interstate and take a break if you feel unsafe. Make sure your rental car is equipped with snow tires, an ice scraper, and windshield washer fluid.
Have a lovely trip -- winter in New England is beautiful, and Woodstock will be magical at Christmas time. Hopefully it will snow for you!
ETA: you also have the option of driving up I-91, but I can't recommend much along the way... it's pretty, largely farmland, but very empty :-) I'd go I-89.
ETA again: added some more suggestions to the above
