you definitely can quilt in the borders. all depends on how much quilting you need for the type of batting used. so far it's a great effort!! don't sweat it. i hated doing basting on the floor so now do it on a folding table. i smooth the backing wrong side up on the table and use binding clips to hold in place. then lay the batting and smooth it. then lay the quilt top on, matching centers and being sure it fits inside the backing size well, then smooth and re-clip. then i either thread baste or pin baste (or use fusible batting or spray basting actually) and move the whole quilt when the center is done. then i finish basting the sides and top and bottom. Then take to the machine to quilt.
keep going, so far you are learning well.