The Shiba Inu meme is based on a 2010 photograph. It became popular in late 2013, being named as Know Your Meme's "top meme" of that year. Doge is a cryptocurrency based on Doge, the Dogecoin, launched in December 2013.
See also: Big Floppa, NAFO (group), Vatnik (slang), Saint Javelin, British scientists (meme), Internet meme.