^That might be so. However, Q is not looking for help, he is sending Wesley for help. So it isn't like Q would have to work with her. The point still stands that it seems like Q helps and hurts Picard whereas Janeway helps and hurts Q. Of course, perhaps Q actually would like to see the galaxy destroyed along with the people responsible for the death of his son so he really would like Wesley to fail.
I think we can see from Q&A that Q has a special relationship with Picard and does not want to see him fail.