You will need permission from the original designer/owner of the copyright. If you do not obtain permission, you risk being sued and potentially relinquishing any and all profits made from the sale of your series. Contact me if you would like to discuss further.
The prior respondent seems to suggest that you always must get permission, and I disagree with that. From Nimmer: "Statutory copyright protection is largely unavailing for dress designs ... a clothing garment constitutes a ''useful article'' within the statutory definition, ... [while] a fabric design is capable of such separate identification and independent existence  a dress design typically is not."
Having said that, you would need to consult with a lawyer if you really intended on publishing a book with your art, derived from these dresses. Why? Because a host of other issues appear. For example, to the extent the dresses are "costumes" - some cases have protected highly artistic costumes as sculptural works. I tend to doubt fashion dresses fall into this, but it is possible. Also, while dresses themselves are probably not protected, the fabric designs may be. You could therefore not duplicate the fabric prints themselves (without permission).
Then, there is the issue of how you got in to the runway show. If that was by a ticket, that ticket can be a contract. That contract might prevent you from making these images (think museum ticket - cases have upheld those as contracts, and thus even public domain art can be prevented from being photographed or copied manually).
Finally, there is the issue of trademark. Even if a dress is not a copyright, it could have trade dress protection (here, the design of the dress would have to be inherently distinctive - again, probably not likely, but certainly possible). Also, you mentioned use of the trademarks of the designers (like "Dior"). There are fair use principles available for use of marks in works of art, but you have to be careful. If the mark is used to identify, that is typically ok, if the mark is used to promote, or is confusing or would suggest a source of affiliation, it is not.
If you are income qualified, you may want to register as an artists at: http://www.mdartslaw.org/ and request a pro bono lawyer for assistance.
Although the previous answer is technically correct, the note's author asked about using the names of the designers along with illustrations of their designs. I would not recommend that action without seeking and gaining permission of the designer.
The following is not legal advice and should not be relied upon to take or refrain from taking any action.
I see nothing at all wrong with creating drawings of dresses designed by known (or unknown) designers, compiling those drawings into a book, truthfully identifying the drawings as representing dresses designed by whomever designed them, and then selling the book.
Whose rights, and what rights, are being invaded?
As Michael notes, creating and selling the proposed book does raise questions that should be addressed by an intellectual property attorney but at root the plan does not offend any rights of which I am aware.