Because it is a smaller top, the quilting should not need that much extra backing - just try to be careful with your quilting. If you only leave 1" on each side, that should free up enough for your binding. Another option is to do a self-binding. I often do this on a baby quilt because then I never have to worry about the baby chewing off the binding! Then just leave 2 1/2" on all sides, after quilting, trim to 1", fold over cut edge, fold over to front and topstitch. This gives you a 1/2" binding that will not come off. Because it is stitched thru, it gives the back a nice 'framed' edge.