It is certainly possible to take a quilt like this apart and re-assemble it with new batting. You would need to first un-pick all of the quilting, and then un-pick whatever stitching is holding the edges together. You definitely would not be "tearing apart" the quilt! You would simply be removing the hand quilting. Since the top is in good condition, removing the hand quilting stitches will not harm it at all.
Since you are used to a thin quilt, I would assume you want to keep a thin batting. Quilter's Dream Request and Hobbs 80/20 are both good choices for either hand or machine quilting. The QDR is flatter; the Hobbs has a little more loft.
If you have never quilted before, it's a good idea to create some practice pieces using cheap muslin and a piece of the batting that will be used in the quilt.