If you want to help your friend, CountessFosco, the easiest way would be for you to invite the girl to stay with you, since you were planning to have her in the afternoons anyway. I have a German friend, and when our children were young, we had various German young people to stay, that my friend referred to us. They weren't Au Pairs, but helped a bit around the house and with children, in exchange for board. Last Easter, we had the daughter of one of our German guests long ago as we were asked but couldn't find anyone who would be willing to have her.
Apart from all the work/visa rules, people nowadays seem to be reluctant to have someone they don't know, stay with them - maybe lives too busy, house too small?