I really love your wall hanging. Did you have a named pattern or your own design? Provided your batting is not too thick, and you're using a quilting/redwork design, then yes - you can embroider through the whole sandwich, and you will not need any stabiliser behind. First you will have to secure the sandwich by either tacking, spray basting or pinning. If using filled designs you would have to do that on just the quilt top with stabiliser underneath, before sandwiching. Make sure your quilt is well supported so there is no drag on your hoop. Please post another photo when done.