I suspect it's just a case of what letters are left. You want a single character to save space on a silkscreen, and I is undesirable as it looks like a one.
Transformers predated transistors which would explain Q as a probably fairly arbitary choice.
Off the top of my head I've seen :
A ?Antenna
B Battery, Bridge rectifier, pushbutton
C cap
CR diode (Crystal rectifier)
D diode
E
F fuse
G
H
I Undesirable as it looks like one
J Jack
K Relay (clicKy thing?)
L Inductor
LP lamp
M Meter, motor, MOV
N
O Undesirable as it looks like zero
P Pot or plug/pin header
Q Transistor
R resistor
RV variable resistor
S Switch (or SW)
T transformer, thermistor
U IC
V Valve/Gasfilled tube e.g. neon, varistor
VR variable resistor
W wire link
X Crystal
Y Crystal
Z Zener