Ummm... some things to think about:
1.) Can you even find skis and boots that size? If you do, does the mountain have an appropriate hill to start (I don't think a lift is a good idea for a toddler, even withan adult. Not only can they get frightened, but they can be squirmy and unpredictable and the lifts can go VERY high and occasionally stop and you have to wait in the air... yikes!). Maybe a gentle slope that either you can walk up or a rope-tow where you can support her, maybe... maybe.
2.) Toddler won't be able to handle it for long. By the time you get the skis, bundle her all up, put the feet in the boots, get out there, snap on the skis and get going, my guess is that you'll have about 1/2 hour in the cold at the most. That's a lot of work and money for a short time. The physical demands of the cold temperatures, heavy clothes, and physical and emotional exertion of dealing with learning to ski is very rough on children and they tire quickly, even if they are having fun.
3.) What about you and DH? He'll need lessons (or lots of your concentrated effort and attention) on a beginner hill. What about baby? You wouldn't be able to split your attention and keep both safe even if a beginner hill were ok for a toddler. The three of you would not be able to really enjoy skiing together.
I've thought about this a lot (we are in the Colorado Rockies and I can't wait to get DS out there!), but I think we will wait until he is more like 3 or 4- when he is a little physically stronger and can at least hold on to a rope tow, follow some basic instructions, keep his gloves and hat on, communicate his needs a little more clearly (ie- my boots are too tight!), etc. I agree with getting kids started early on stuff like this, but I'd wait. Kids as old as 8,9,10 pick it up with no trouble at all. Waiting until she is 3 wouldn't be so bad, I don't think!
If I were you, I'd go with DH (either bring along someone to watch baby in the lodge where you could pop in frequently or arrange to go with another couple and share kid duties!) and get him going- some lessons or you teach him. Once he learns, you can enjoy skiing together and in a couple years, he can help out when it's time for kiddo to hit the slopes and you won't have to try to help both of them together. And by 3 or 4, they might be ready for their own lessons or ski-school, giving you two a half hour or hour to enjoy the slopes too before family time.
In the meantime, what about x-country skiing? Or snowshoeing? Baby can ride in a sled if the equiptment is not available for her and she can still enjoy the experience and it doesn't take a whole lot to learn...