After I soundproof my bedroom wall with QuietRock, will I need to somehow soundproof the floor?
For insulating against sound between floors in our condo builds, we use the following from top down:


Carpeting where possible
Homasote on top of the subfloor
Fiberglass insulation in the ceiling
Resiliant channel to hold the drywall ceiling off of the joists (also known as sound attenuation channel)
Standard drywall ceiling, installed with 1" tight threaded drywall screws into the resiliant channel


I think the part you're looking for is the Homasote. If you have access to, and were concerned with, the ceiling below (which from your comments on the garage, this doesn't seem to be the case), consider the resiliant channel.