There's no reason why a keen DIYer with a few tools can't do this sort of job. Prior to cheap self-levelling lasers this sort of job required string lines and 6ft levels (or a shorter, accurate level strapped onto an accurately planed length of straight carcassing) and wasn't anywhere near as easy a job to do. These days with a cheap self levelling laser and a home made wooden staff the job is relatively simple.
I'd sound two notes of caution about this - firstly hitting an 18mm edge more or less dead centre with a screw through a sheet of plywood or chipboard isn't necessarilly that easy, especially not over the full extent of a floor, and secondly it really isn't advisable to screw into the edges of plywood because it can delaminate all too easily. In fact the quality of modern Chinese-made construction hardwood plywood is so poor that it is almost a foregone conclusion that it will end up delaminating if you edges screw, even if you pre-pilot. Something like 3 x 2in (70 x 44mm) or 4x 2in (90 x 44mm) CLS is not only a bigger target to aim at but it won't just delaminate like plywood canEasiest way is sister the joists with inch ply (rip it down to 4" or 6" wide strips) then screw your floor to the ply ededge.