The light is fairly lovely, yep. Disagree that it's underexposed, the highlight is blown out and there's no blacks to speak of, could probably have used a smaller aperture or faster shutter (and the mucked around in post to bring the skin tones back).
The light in the room is actually still a trifle harsh. Notice that the shadowed side of the face has quite nice tones, even a little on the dim side, but that lit side is blown out - patches of pure white.
It does capture the feel of the light quite well, I don't fuss about blown hilights as much as some people do. If you love the light in the room, use a reflector on the shadowed side (a relatively flat white object just out of frame will be fine, you'll be startled at how much lighter it makes the shadowed side of the face) and use a smaller aperture, for less total exposure. This will tame the highlight some, without making the shadowed side of the face go too dark. Well, it will, if all goes well.
Alternatively, wait until the light through the window is somewhat less intense, perhaps an overcast day, or a different time of day. You run the risk of making the whole thing too dark in this case, though.
There's stuff you can do with flash as well, but it sounds like you want to use the natural light, since it's the light you love.