Those of you who are alert will have noticed that my Pprune nic comes from the international aviation Q code, so take it from someone who knows.
Islander Jock 4Screwaircrew are correct. The Q code was developed by the ITU around the turn of the century to standardise morse code communications and understanding between different nationalities, particularly when Morse Code started to replace Semaphore as the prime means of communications in the maritime environment. The secondary purpose of the Q code was also to abbreviate routine but long worded communications as Islander Jock has also correctly demonstrated.
I've never heard of the "Question Normal Height" theory, so I don't think that is right, although some Q codes become obvious after a while eg QFE (request "field elevation" pressure).
Along with QNH (sea level pressure), other codes that were most often used for aviation were QDR or QTE (request DF), QDM (DF inbound course), QNE (flight level based on 1013 HPa), QFE (aerodrome pressure), QTK (request GS), QRK/QSA (how do you read), QSY (freq change) etc. For example, if an aircraft wanted to know when to change frequency, it would send "QSY?' in morse. The ATS unit would respond by sending back in Morse Code "QSY125.6" or just simply "QSY" (if the unit believed the pilot already knew the frequency) which was both an acknowledgement of the aircraft's request (the pilots didn't do the communicating in those days) and approval to change. The full list of aviation Q codes can be found at
http://www.kloth.net/radio/qcodes.php
Radio telegraphy (RTG) was used extensively for aviation communications in Australia and overseas right up to the late 1940s and early 1950s, and many of Australia's old Flight Service (Aeradio) Units only ever communicated with aircraft using Morse Code. In fact Cocos Island FSU was still using Morse Code for the relaying of weather, flight plans etc between Perth and Mauritius even as late as the 1980s. I also believe that the NZ Airforce were still training their radio operators on HS748s to use RTG on international HF frequencies also up to the mid-1980s. If you want to know more about this aspect of aviation history please visit the Australian Civil Aviation Historical Society website located at:
http://www.airwaysmuseum.com/
Other informal codes which one also comes across today (sometimes in SMS messages) also are hangovers from MC days eg CUL (see you later); R (Regards).