Blue Stuff,
No, the Q (and Z) codes were not avation-specific. An instructor of mine in my pre-aviating days gave me a potted version of their W/T origins, and opined that Q and Z were the best with which to begin the trigraphs as they are the longest Morse letters that won't easily be confused (by a tired listener) with numbers. Bear in mind that a lot of codes were sent with quantifying figure-groups immediately afterwards. Most users only needed a small easily-remembered selection of the codes for normal ops - the complete list would've taken up too much room in the average W/T operators workspace.