is the laundry room part of the regular home? Meaning, can you go in the attic and access the laundry room from the attic? Do you have central AC?
If the above are all answered "yes", then all you need to do is to insert a "T" into a AC duct in the attic and attach an additional duct and run it to the laundry room and affix it to a register that you install. Doing this project is about a 3 on a scale from 1 - 10, 10 being the hardest.
If the laundry room is not accessible, then consider just adding a reversed fan in the walls with grid covering it from the outside for security.