Insulating Garage Ceiling?

We just had our first child, and his room is right above the garage. It is noticebly colder in his room, especially the floor. I used the plastic window kits and that helped, however, the floor is still extremely cold and I would like to at least check the insulation in the garage ceiling. Right now there is drywall on the ceiling, but I have no qualms about ripping it down, not real worried what it looks like. What should I look for...I believe there is very old (50 years) fibergl insulation but i'm not 100% sure. If there is the old insulation there...should I look to replace it? If so, with what R value...Is this a project that someone without specific experience in the field could complete? I'm pretty handy but certainly not a pro. I'm not worried at all how it looks in the garage.