"I Have No Idea What I'm Doing" is a catchphrase often used in image macro captions featuring photos of animals, typically canines, posed as if they are performing tasks associated with humans, in a similar vein to "Yes, This is Dog" and the Dog Fort comic series.
The earliest known appearance of the photo of a Golden Retriever posing with a camera appeared on the Hong Kong Wordpress site Photoblog on November 20th, 2010. On February 27th, 2011, a photoshopped version was posted by Ben Grelle (a.k.a The Frogman) to his Tumblr blog with the caption "I have no idea what I'm doing." The post received over 5,000 notes in less than a year.
On March 3rd, 2011, Frogman's image was submitted to Reddit and reached the front page accumulating 3,609 up votes prior to being archived. In the thread, Frogman responded with a complaint that his watermark had been cropped out of the image, and provided a link to his original post.
The earliest known instance of the chemistry dog with the "I have no idea what I'm doing" caption was posted to the Lolabego Tumblr on June 17th, 2011.
Bailey the Golden Retriever
On December 2th, 2011, an image of a dog sitting at a laptop accompanied by the catchphrase was submitted to the /r/funny subreddit and reached the front page accumulating over 4,500 up votes within 6 weeks.
On October 15th, 2014, Redditor Golden_Bailey submitted a photo gallery of the dog titled "Remember the 'I have no idea what I'm doing dog'? I am her owner and here is a small album of more(better) pictures of her" to /r/aww. On January 8th, 2018, Redditor Golden_Bailey submitted another set of photographs identifying the dog as Bailey to /r/pics, where the original desk picture was included (shown below). In the gallery, Bailey's owner revealed she had died due to complications from bone cancer in early 2016. Within 24 hours, the post garnered upwards of 124,000 points (88% upvoted) and 2,300 comments.
Between 2012 and 2013, the phrase continued to grow in popularity as the scope of its usage began to expand beyond photographs of clueless-looking dogs.
Search queries for "have no idea what I'm doing" picked up in March of 2011, the same month the original Frogman instance was posted.
 TheFrogman.me – The Frogman – Comedy, photoshop, kittens, & corgis