It looks like the edges are still loose. You could applique the top edge to border pieces, add a border to the backing also, and piece the batting.
To piece the batting, peel back both top and backing fabrics and pin out of the way. Layer your quilt batting on top of another piece of batting. Use rotary cutter to cut through both battings in a wavy "S" line. Remove the extra batting pieces and the new batting and old batting will butt perfectly together. For a small quilt like this, I would probably hand tack the battings together using a tailor's stich, although you could also machine sew them together with a wide and long zigzag stitch.