What do I need to fire proof a room added onto a mobile home?
Follow the stove manufacturer's instructions for clearances. It will tell you the fire rating requirements expressed in "hours" (or material type) for surfaces around the stove depending on clearance.

2 layers of 5/8" Type-X fire-rated gypsum board (drywall) gives a 2-hour fire rating to a 16" on-center wood stud wall. Surface treatments like stone, brick, tile, durock, sheet metal, etc., will give you aesthetic options. Check with your local code enforcement authority, they will give you information on local requirements. If you follow manufacturer instructions and local code then your insurance company will accept that if you show them.