Some years ago I was contacted by a solicitor's firm who needed to get the accounts data of an old computer of theirs - they said that it ran under QDOS.
However, it wasn't QDOS as we know it, nor was it the 'Quick and DIrty Operating System' which was the precursor to MSDOS - it was a QDOS accounts package which used a completely different disk format.
That said, I was able to track down someone from the company who originally supplied the accounts package and he found out some tools to transfer the data, so I was still able to help.
The QL was still first with its use of QDOS - what a shame that the name was not trademarked (so far as I know)