I would do, as others have suggested, vertical lines - inside the panel. I have no experience with doing 1/2" to 1" strips. I would do two inches or so, if you are using a batting that allows wide quilting space such as warm and natural. If I was brave, I would attempt to follow the lines of the tree trunks. I would use a disappearing thread on top and a thread that blends with the backing in the bobbin. I would sew on the line around both sides of the "picture frame". I would outline the squares on the sides. I would do something different on the border area outside the bird squares - maybe a diagonal strip or something that undulates if your machine has that stitch (doing that well freehand is difficult).
Good luck and let us see your result.
bkay