Thankfully, all of the information I needed could be found on doctorwhoscarf.com! To begin with, the site lists specific yarn colors by brand that match the colors of the original scarf. I had to special order some of the yarn since some of the colors were very specific and I couldn't find them in stores! Then the site has several different knitting patterns for various yarn weights and scarf variations to reflect the changes made to the scarf over the course of the television seasons. Apparently the actual scarf used on the show got stretched out over time so they periodically removed sections to make it shorter. I used the Orginal Worsted Weight pattern... which also happened to be the longest. It ended up being nearly 10 feet long!
It took months and months to knit, but the end result was pretty fantastic!
The only place I could get a full-length photo of it was on the stairs!