I would iron heavy-weight interfacing to the back of the main body fabric before quilting it with a really close up and down lines design. Both of those things will give it more strength and stability. I would leave the seam allowance without the interfacing so it will be easier to sew the bag together. Get what I mean?
The fabric itself would drag down the sides using that heavy of a fabric. I see why you chose it though. It is really pretty.