If by gutted you mean the wall plaster is removed then this will be relatively easy and not expensive, you potentially could do it yourself- Roxul Safe and Sound rock wool insulation batts installed in the wall stud spaces between laundry closet and bedrooms. Same product installed in the downstairs ceiling joist spaces- leave an air gap on either side of the insulation batt- and for a little more expense have the drywallers install resilient metal channels to the bottom of the ceiling joists and install the drywall to the channels, thus isolating the drywall ceiling from transmitting sounds to the rooms above. Rock wool is mostly basalt rock basically spun like cotton candy, it is fireproof, increasing the fire resistance of your walls and ceilings and absorbs noise- hence the Safe and Sound name. You tube has some installation videos, good luck with your renovations, stay calm, things might take more time than you hope but it will be great once completed.
Q