Do I need to quilt this?
 

I just finished a quilt that is one piece of fabric on the front (cotton/poly blend) and fleece backing. Since there is no batting in the middle to shift, do I need to quilt this?

I would to hold the two together.

I've made this type of quilt as a baby quilt and quilted it. I was afraid the 2 pieces would shift in the wash. I did minimal quilting with my walking foot and decorative stitches.

I totally agree. You don't want the possibility of it sagging.

Yes, use a walking foot and a simple design to speed it up.

I would want to keep the two layers together so it won't start shifting and sagging.

Maybe just a quick cross hatch would work. It does not need to be too closely quilted

If you don't want to quilt it, you could tie it in a few places.

Years ago I put 2 fleece fabrics together and then added what I guess you would call "hash tags" in various areas to keep the 2 layers from shifting. I just used what ever little design was on my machine such as a heart or diamond and it seemed to work as these fleece blankets are still being used and have been washed un told number of times.