That will certainly provide fire resistance with the right thickness of plasterboard, but simply adding rockwool between floor joist will not achieve the required decibel level reductions, particularly as any testing will be done without the carpet and underlay.
The gypsum plasterboard “White Book” details all the construction methods and ratings, well worth a look.
In our conversions we added a double layer of 12.5mm gypsum soundboard, fixed to a metal frame suspended ceiling grid on acoustic hangers, 100mm of rockwool over the ceiling grid retaining a 300mm minimum air gap to the underside of the floor. Then adding a floating floor on rubber isolating membrane on top of the existing floor boards, plus a fibre board underlay to laminate flooring. Our test results were the best ever produced in our area, outside of an organ factory with 300mm thick concrete floors, and exceptional considering it was a conversion of an old building. Because the laminate flooring is a hard surface, the tests were conducted on top of it, thereby including the additional layer of sound reducing fibre board underlay.
There are a few tricks to achieving these results including sealing up every gap around the perimeter of each layer of ceiling boards with silicone, as airborne sound travels like water. The airgap and acoustic hangers are needed to mitigate impact sounds.
I appreciate this may not be possible in regular houses with limited ceiling heights, we were lucky enough to have 11 foot high ceilings in the original buildings. There are construction methods to address the issue in properties with low ceilings, again detailed in the White Book.