I'm not sure of any exact date that these jokes started, but they were definitely around by the time Napoleon took full control of France. The idea of the short Napoleon began with his own Imperial Guards. Like the stereotypical bodyguards today, they were big and strong and well above average height. They were also constantly near Napoleon, so he looked short by comparison.

Then his many enemies, mostly the English, took and ran with it. Like today, political cartoons were very popular and well known for exaggerating certain traits to get their points across and sell the idea of going to war against him constantly. So you end up with super short Napoleon like in these German cartoons: http://chnm.gmu.edu/revolution/d/167/ http://chnm.gmu.edu/revolution/d/169/

His official recorded height didn't help matters. Officially, he was 5'2"...in French standards of measurements. At the time their foot was longer than the English (now American) foot. So your average British citizen hears that Napoleon is 5'2" and sees cartoons portraying him and calling him short and the misconception is born. And historians can keep joking about (and correcting) this. Hark! A Vagrant! did a funny cartoon on this here: http://www.harkavagrant.com/index.php?id=320 and CGP Grey summed everything up well in his "5 Historical Misconceptions" video here: http://www.youtube.com/watch?v=sYzfKiIWN4g&list=UU2C_jShtL725hvbm1arSV9w