It hasn't been done randomly or just for fun, it has a very distinct and purposeful reason behind it.

The current format of the keyboard was devised long back in 1870’s by a gentleman named Christopher Sholes. Though, it definitely was  not the first format to come up, it didn't take much time to switch to  this one. Starting with lexicographic order i.e. A-B-C-D-E-F, after  various trials and errors and taking hundreds of cases, Christopher  Sholes gradually reached the Q-W-E-R-T-Y. It was really well received  (evident from the fact that we still use it).

When the typewriter  was invented, it used a metal bar to hold the character alphabets and  the other end of the bar was attached to a linkage carrying a carriage  with the coated ink. When a key was struck, it would emboss its  character on the paper placed beneath the carriage. However, when an  operator learned to type at a great speed, a certain flaw invoked. When  two letters were struck in quick succession, the bars of the typewriter  would entangle and get jammed.

Christopher Sholes found a way  out. He proposed that the letters of frequently used letter pairs should  be in different rows. For example, ‘C-H’, ‘S-T’, ’T-H’, ‘W-H’ and more.  He also formulated that to speed up the typing process, there has to be  a regular alternation between two hands. So observing thousands of  words, he placed the letters in way that most words would make use of  both hands.

He also observed that almost every word in the  dictionary carries a vowel. According to him, the most frequently used  vowel was ‘A’ and the most frequently used letter (non-vowel) was ‘S’.  So he placed ‘A’ and ‘S’ together and chose to keep less common letters  like ‘Q’, ‘W’, ‘Z’, ‘X’, ‘C’ around these. This was complemented by  placing fairly common letters like ‘M’, ‘N’, ‘L’, ‘K’, ‘O’, ‘P’ at right  extremes to create a perfect alternation between both the hands.

All these factors tested with thousands of trials gave us the format that we still use and perhaps would be using till eternity.

source: quora.com