I would use graph paper to make log cabin blocks for a dollhouse and paper-piece to the graph paper. This would be the easiest way to get nice even blocks.
Be sure to use fine thread for piecing -- 60wt or finer.
If it requires batting, I would use a single layer of flannel (washed and dried a couple of times first).
Also use fine thread for the quilting (100wt, or at least 60wt), and don't make the quilting lines too close together. I once made the mistake of doing a close stipple on a doll quilt (using regular 50wt 3-ply thread) and the thing came out stiff as a board. To keep the quilt soft, use fine thread and minimize the amount of quilting.