Carol,
Having made a Sunbonnet Sue with appliqued blocks, I think I would machine stitch (I used a zig-zag stitch) around the edges and used transparent nylon thread. Then, I think I would probably sandwich everything, quilt just on the edge of the white using white thread before you get into the background petals of your design. I might even quilt in the white surrounding the pink center. That should be sufficient to stabilize everything and keep your batting from shifting. Of course, I am sure there are those who are far more experienced. I am just a rank amateur!
Jeanette