Messages were originally Morse in plain language; as short codes developed it was useful if they started with something distinctive in the middle of the string of characters. Q is a good one because it is uncommon, and also almost always followed by a U, so if a Q came in the rapid-fire string, followed by say an N, then the recipient realised that it was a code promptly.
With a Q starting 3-letter codes you only have two left for the actual message, so all sorts of informal aide-memoire sprang up to know them by. I've heard all sorts of different ones for QNH and QFE over time. Remember also that it is primarily a shipping approach - by the time W/T came along in aircraft, the shipping users had got all the good codes.