What is a knitted cotton-warp quilt and what is it made of?
Believe it or not, I found a forum for knitters. I've pasted the link to a discussion about cotton-warp quilts on that site below. When we think of quilts, what usually comes to mind is a patchwork of cotton fabrics sewn together, not knitted. For Lucy Maud Montgomery, however, a quilt seems to have been any kind of bed covering. So what Rachel Lynde was knitting was probably a large blanket.
Another web page for knitters has this: "Cotton warp is a kind of cotton thread. It's used for the warp threads in weaving. It is about the same weight as a sport weight woolen yarn." This site, knittheknits, has pictures of blankets of this type.
I hope this helps!