Although as I read the answers, I'm glad to know my suspicions of L.M.'s Hepburn-hood are now confirmed, I'd add that "My Fair Lady" is more the Edwardian era (Shaw wrote "Pygmalion" in 1913); even then, the costumes are more Cecil Beaton's flights of fancy than a historically accurate depiction of common clothing. Academy-Award-worthy, true.
Very correct, however, that Ms. Hepburn's manners on or off stage were uncommonly Victorian and Edwardian for the 1960s. And thank goodness for it.
Regarding the film's men's clothing, I've always thought Harrison and Brett donned historically accurate Edwardian softer-shouldered bespoke, along with correct shirts; but that's Savile Row for you.
Regarding Victorian styles, see the hundreds of recreator pages online (shoot for the 1840-1860 Dickensian era), go to your nearest university library over a weekend (should be at least five Victorian costuming books there), or check out or buy used books such as /Victorian Costuming/, by Winter and Savoy.
http://www.amazon.com/s/103-8718662-2403000?ie=UTF8&keywords=Victorian%20Costuming%20by%20Janet%20Winter%20and%20Carolyn%20Savoy&index=blended
Note that American and British Victorian styles differed, as did dress by decade.
Comprehensive portal site:
http://www.victoriana.com/Victorian-Fashion/
http://www.victoriana.com/antique-marketplace/Fashions/children.htm
http://www.victorianamagazine.com/
Rather humorous:
http://en.wikipedia.org/wiki/Image:1868-skirt-lengths-girl-ages-Harpers-Bazar.gif
See the women's and children's sections of these articles (13 would likely be considered a young woman in those days), with the accompanying paintings, for thoughts:
http://en.wikipedia.org/wiki/1840s_in_fashion
http://en.wikipedia.org/wiki/1850s_in_fashion
http://en.wikipedia.org/wiki/1860s_in_fashion
Also see the references and external links at the bottoms of those articles.
Hairstyles for American women:
http://www.victoriana.com/VictorianHairStyles/civilwarhairstyles.htm
Some fun photos, costume and language guidelines, comportment tips, and other slightly over-the-top, fun stuff for recreators of British Victorian is at the San Fran Dickens Fair site: http://www.dickensfair.com
http://www.dickensfair.com/costumewomen.htm
http://www.dickensfair.com/languageguide.htm
Similarly, a tremendous and serious collection of brief social-history reading material to help get in character (British):
http://www.victorianweb.org/history/sochistov.html
And readings about American Victorianism:
http://www.victoriansociety.org/
Including this page of clothing links:
http://www.victoriansociety.org/resclothing.html
Canadian exhibit documenting Victorian clothing variety in photos:
http://www.mccord-museum.qc.ca/en/keys/webtours/VQ_P2_17_EN.html
And what collection of Victorian fashion links would be complete or accurate without the V & A?:
http://www.vam.ac.uk/collections/prints_books/victorian_sentiment/index.html
http://www.amazon.com/Nineteenth-Century-Fashion-Detail-Lucy-Johnston/dp/1851774394/ref=sr_1_1/103-8718662-2403000?ie=UTF8&s=books&qid=1188369105&sr=8-1
http://www.vam.ac.uk/vastatic/microsites/victorians/finals/publications.html
http://www.vandashop.com/product.php?xProd=18&s=1
http://www.vandashop.com/product.php?xProd=45&s=1
http://www.vandashop.com/product.php?xProd=28&s=1
http://www.vandashop.com/product.php?xProd=31&s=1