Well, I tried. I submitted my proposal and manuscript to a literary agent who I had set my hopes on to mediate a contract on my behalf--only to receive a prompt reply that he did not represent children's books. Hmm...back to the drawing board, I guess.
A drawing board is an architect's or draftsman's table. According to Phrase Finder, the phrase "back to the drawing board" has been around since the WWII era and was used in conjunction with a failed design that needed to be tweaked.