So I am almost finished (just need to do the binding, which I am going to do tonight) with my first quilt. I had no sewing experience, and had never made a quilt. Taught myself using Youtube tutorials, this forum, blogs, and a book. I made a one block wonder. I know you said no triangles, but I am just going to suggest this one, because I found it to be a great first project for the following reasons. 1. you can see each kaleidoscope coming together as you sew, its immediately satisfying, which gives you the drive to want to continue. 2. Its repetitive so you can practice a lot. 3. Because it is so busy, it is very forgiving of flaws, so I can look at my quilt without cringing, which is a great feeling, and makes me want to do more. 4. I found it really FUN to make, and I say this as someone who was NOT expecting to like quilting at all. Seriously. I really think a big part of the reason I like quilting is because I chose the right style for myself.
That said. I think the best advice is have her look at pictures of quilts and ask her what appeals to her. Find out what she likes in a quilt and then try to find an easy pattern that she likes the style of, because when you make something you like and fits your style, its easier to survive the frustrations of being a new quilter.