A one hour fire rating is generally required for multifamily housing where there is a shared wall dividing two separate residences. Some garage to living area walls also can require the wall be protected. These walls use a special 5/8" Type X drywall.
In your initial question, it sounds like you are in a single family home.
Let me know if the room on the other side of the laundry room is another persons living area. Hope this helps. thanks.