I have had this idea (and the dress!) for months, and finally had time to lay everything out and start sewing. I found these pretty colored doilies on Etsy.
I layered the doilies in different sizes and colors and then pinned them where I wanted them to go.
I hand-stitched each one all around the edges and within the doily, too, to hopefully prevent fraying and catching on things. (I definitely plan on handwashing.)
I used an off-white thread on each one (tiny stitches) so I didn't have to come up with so many different colors of thread and the stitches don't even show.