How thick is the wadding in your quilt? If it is a thicker, softer, wadding I believe you may have more difficulty with this happening. If this is the case, I don't think pinning will be enough to stabilise it for quilting. You may need to spray baste and also do some large basting stitches by hand or machine to keep everything in place before you start seriously quilting. Use a walking foot for stitch in the ditch and don't sew in the one direction all of the time, so that you are evening up the "push" direction of the fabric.
It is much easier to quilt with thinner wadding. All the best with your efforts.