I've made three quilts that have Minky backing. See the third picture in the below linked post and read the post where Minky questions are asked and answered. I don't do the quilting but my LAQ reports that it quilts just fine. I love it for the backing - it looks nice and feels wonderful. I do have to be careful when putting on the binding because the Minky is slippery. Just have to control it and stitch slowly.
http://www.quiltingboard.com/t-91087-1.htm