I have found a great link showing you the colours required to make an authentic looking Doctor Who Scarf. Check out Doctor Who Knits.
Due to copyright protections, I cannot show you a picture here on my blog. If I were you you, do the stitches in Single Crochet. Follow the colour schemes. Be aware the sizing may not be in the same units you are used to. You may want to use the recommended hook size shown on the yarn label packaging.
While the scarves are exceptionally long… so long you could actually trip over it, these scarves are popular nevertheless.
For further inspiration and ideas, please visit my website, The Crochet Crowd.