QQ is the way to go; DSTL don't do flight test work as such. Or you could consider working for the flight ops department of one of the other DAOS approved companies such as BAE Systems, Marshalls, FRA, Westlands or Britten Norman.
The road to FTE is a long one; at QQ typically about 4 years as a trials officer as I understand it, during which you may not even get to fly on an aircraft (depending on your work area and technical specialism), then you need to get selected for ETPS. Each year there are several more applicants than places on the course, and it is competed.
If you are serious about doing this, I suggest you get a PPL and as much practical hands-on aviation experience as you can. Bear in mind that the QQ graduate scheme is apparently a very good one, with many more applicants than places, and you may not even end up at Boscombe. Probably best to apply to as many aviation companies as you can; if you get a good grounding in aviation at a major aviation manufacturer you could always move to QQ later on.
Best of luck, flight test is a great profession to be in and with hard work, commitment and a bit of luck you could end up being a FTE.