We did CTC last year and for this reason didn't ever research beyond the topic and "keywords" given in the guide. We found this to be a safe way to go about researching, as I know how quickly the Internet can take us and our dc places we don't want to go. Carrie tried hard to check out every keyword search she planned, so I feel safer with those, though I know it is still my responsibility to oversee it carefully. We have a few rules in place - dc may not be on the Internet when we are not right there in the room with them. Dc are only on the Internet for school-related research right now. Computers will never be allowed in their rooms, and can only be used on the main floor in open people-populated rooms, when we are right near them. We have talked about all media forms and using sound moral judgment in using them the way God would want us to use them. So, just like we have to use moral discernment when using the computer, we also need to within choosing books, magazines, music CD's, radio stations, activities, friends, etc.
We've also told our dc (especially since we have boys) that there are inappropriate pictures of women and men on the Internet, where they are unclothed, and that this is not only sinful, but it is also a temptation to us that we need to guard against. One of my oldest sister's friends has 12 dc she homeschools, and has graduated several already. She said the wisest thing she and her dh ever told their dc was that there would come a point in their lives where they would probably be strongly tempted to look at pictures of people without their clothes, and that when that happened, they wanted their dc to tell them immediately so they could talk about it and help them through it. We have told our oldest ds the same thing, and try to remind him of it once and awhile so we are there to help when that temptation arises. Accidents do happen, and though I'm sure you've already said something akin to this, she should understand that her seeing that image was not planned, and because she did not make a conscious choice to seek that out, her seeing it was not her fault, and not a choice on her part to sin. I'd just let her know you've had this happen before as well, and that it's just a reminder to be careful when using any form of media. It's not a reason to stop using all types of media, but instead a reminder to consciously choose how to go about it. So, staying just on the first search site of the keywords in CTC would minimize this happening, and if she would like to further research something on a different site, perhaps you could let her know you'd take a minute to check it out and make sure it seemed safe before she looked at it. One other way around this would be to get a children's encyclopedia to use instead or to use a set of child-friendly encyclopedia CD's. Though I'd be inclined to still do the Internet research as some point, as I feel this is an important thing to teach our dc as we are by their side.
HTH - but you are wise to guard what your dc read and see carefully! It is a difficult responsibility we all have as parents that is easy to forget sometimes. Thanks for reminding me of this all-important task again!
In Christ,
Julie