OH...I love that fabric! My kitties need a couple of kitty beds, so if it were me, I'd make a cute, pieced top out of that fabric and coordinate it with some other solid fabrics for the sides and bottom of the beds. In this case, I'd quilt the top. However, if I were going to make a blanket quilt out of it, I'd just tie it. I love tied quilts and I don't think that those dotted lines would have any bearing. They just look like part of the artwork. Have fun with that!
~ Cindy