I'm also working on that exact costume! Well, I'm commissioning someone to make it for me. I suggested burlap, but she said that monk's cloth might work too. No idea what monk's cloth is, but she's the expert. Just bought my purple colored contact lenses today (thought I should stay somewhat faithful to the book).
I was surprised as well that there aren't more Game of Thrones cosplayers out there. I couldn't even find that many pictures of her in that outfit. I had to scour every episode. Best of luck on your costume! Mine should be done in time for PAX.