The use of “Q” to identify transistors in schematics appears to have been common in American practice and from a very superficial search, it may be dated back to 1959 January at least, although I’d guess that it originated before then. A deeper search of the late 1950s American magazines at:
http://www.americanradiohistory.com/ might reveal its origins.
In the UK, “Wireless World” (WW) magazine was using “Vt” in the early 1960s, as for the 1961 and 1965 versions of the Dinsdale amplifier. By the time of the Bailey amplifier in late 1966, it had changed to “Tr”. I’d guess that the reasons for that change could well have been provided in the pages of the magazine somewhere during 1966. WW evidently stayed with “Tr” at least through 1998, that being used in the Slifkin & Dory Synchrodyne/Homodyne article of that year.
Amongst the UK equipment makers, the situation looks to have been rather entropic. Here is a small and random sampling from the data readily to hand:
Eddystone started with “TR” for its 960 receiver of 1962, and stayed with that at least until its 1650 of 1984.
Leak used “T” for its early solid-state amplifiers (Stereo 30, Stereo 70, Stereo 30 Plus) but then switched to “VT” for its 1969 Stereofetic FM tuner. But perhaps surprisingly, it had used “Q” for the stereo decoder section of its Troughline Stereo tuner.
Rogers used “T” for the first edition of its Ravensbourne amplifier (“TR” was used for the transformers, including the quadrifilar driver), but then changed to “VT” for the first editions of its Ravensbourne 2 FET FM tuner and its Ravensbrook amplifier. The Series II version of the Ravensbourne tuner used a mix of “T” and “VT”. I don’t know what it used for its MPX decoder, which was its first solid-state product. In the case of the first Ravensbourne tuner, the Fairchild µA703 ICs were also labelled as “VT”. The Ravensbrook FET FM tuner used “TT” for RF transistors (and fets) and “TA” for decoder/AF transistors, but its RCA ICs did not have letter labels.
Quad started with “Tr” for its MPX decoder of 1963, and stayed with that (or “TR”) until 1982, when the Quad 34 and FM4 both used “T”.
Sugden used “VT” for its early equipment (A21, C51/A51 and R21/R51).
Racal used “VT” for the RA1217, but “TR” for the RA1772, and then “Q” for the RA1972.
Marconi used “TR” for the Apollo (1970) but “Q” for the Oceanic (c.1984).
GEC used “VT” for the RC410-R, as did Plessey for the PR155, then “TR” for the PR2250.
From that one might deduce that “VT” (or “Vt”) was popular amongst the UK makers in the 1960s, with a swing to “TR” (or “Tr”) coming later in that decade. The earliest I have for “TR” right now is for the Jason FMT4 tuner of 1960, which used a solitary transistor as part of its amplified afc system. But a deeper search would likely reveal earlier examples.
Cheers,