I think the timing should be when the child first notices that she needs to type more than a few characters per computer session. You nearly don't need the keyboard for painting, surfing, and goofing around. You do need it as soon as you want to interact beyond using the mouse.
I wouldn't throw an unlabeled keyboard at anyone -- it's not particularly motivating to try to remember 100 keys, or at least the ~50 she'll need for writing.
Rather, I would encourage typing games. Let her hunt and peck for starters, it's a good enough way to learn the location of the keys. Take the focus from the keyboard and have her want to move her eyes to the screen instead.
Google knows many typing games, and there are also some very good typing tutors around -- I've had the best success with the Ten Thumbs Typing Tutor (the newest version even lets you type out song lyrics which might be cool for her). If you've got Linux then there are also several typing tutors built in or available for free.
What helped me type faster was not a blank keyboard, but a wanting to type faster because typing slowly kept me from progressing through the adventure game I was playing. Today's adventure games have a mouse, unfortunately, so you need to look for other typing incentives. (Try asking that on superuser.com.)
For added geek bonus points, you could also consider whether to train in Qwerty at all. Some people think that the Dvorak layout is more comfortable. I didn't say better because that's a near-religious debate, but Dvorak is much more convenient to type. The biggest problem is that if you prefer it, you'll be swimming upstream forever against the force of ubiquity that Qwerty is.