since your design doesn't have any sashing strips you can do the following for quilt as you go.
make each block a quilt sandwich (top, batting, back) and quilt as desired.
then join the blocks together either vertical or horizontal rows (do it whatever way you prefer).
then trim down some of the batting on the seams in the back, press seams open, and whip stitch in place or you can use water soluble 1/4 basting tape.
then to cover the seams on the back - cut strips 1.5 inches, press the raw edges in to meet in the middle (its a bias strip without being cut on the bias).
then hand stitch these fabric strips across the seams on the back with whatever stitch you like.