Poor girl 
I adopted one of mine privately, everything worked out well (and he's most definitely a much happier boy now). Unfortunately, the common shelter rules regarding childrens ages led to me seeking to rehome in this way.
I've since found a rescue which is happy to (using their discretion, obviously!) rehome to families with young children.
Furthermore, a quick scour of 'dogsblog' using the search criteria of 'good with children' brings up many family dogs looking for homes within rescue/foster and I wouldn't rehome privately again.