Flattery gets you everywhere.
The sounds extracted from the PAK, zipped up:
http://jmtd.net/tmp/sounds.zip
also included is a CSV which conveniently lists the sample and bitrates for each sound. (by me, I should add.)
If you want QTest itself, this link works
Qtest Download
I had some trouble extracting the PAK file using conventional tools as it seems the PAK file format might have evolved between this and the final release of Quake.
Next up, I'm going to inspect the quake leaked pre-release beta and the half life alpha which apparently has unused quake assets in it too.