It is interesting that Q sends Wesley to Picard and not Janeway saying, "Do what I always do- go bother Picard." Seems Janeway has been more helpful than Picard in major crises.
It took Janeway several years to cross 70,000 light years, Picard got the Enterprise home from 2,700,000 light years away in 45 minutes
, he even had time spare to drink a bottle of wine and make sweet sweet love to a young ensign.
Q knew that Wesley needed the A-Team to save everything.*
* more seriously, the story partly relies on Wesley's connections to the characters as TNG characters.