Great idea! Your rug looks terrific! You've given me inspiration to try one myself. It's going on the bucket list.
I don't see the, "under rug," in the picture. Personally, if it were me...I would not use one of those waffle weave rug pads. I had one for a regular rug and it was always a mess...scrunching up, folding over, peeking out from under the rug, crumbling, tearing, etc. I finally threw it out. I don't even think that it helped keep the rug from slipping that much. If your quilt-rug isn't getting hard wear and it's not in a high traffic area, then I'd just let it go bare underneath.
~ Cindy