I'm transgender but never been via DOH, so can't help directly, but I have been to places I really shouldn't have gone to (Zimbabwe during the Mugabe regime, as a British citizen being the stupidest).

Having all your documents in order and having SRS, I personally would accept the transit. You have two issues of concern: anomalies in the groin area on body scanners (won't affect you) or any kind of extenuating circumstances, such as you having a heart attack and requiring hospitalization while transiting DOH, which would be significantly less pleasant. I did read somewhere (although can't find it) that Qatar only enforces these policies against Muslims, so if you aren't Muslim, there's a good chance you're exempt.

I'm becoming more and more risk averse as I get older, and as I'm non-operative I probably would avoid DOH myself. But as an anecodate, I've found that the more hostile a place is to trans people, the less likely they are to know we exist.

If you are travelling through areas that are less than welcoming, you may wish to purchase something like MedJet Assist, which advertises private evacuation in a medical emergency 'regardless of medical necessity'. Then if you do end up hospitalised, you can get out as quickly as possible.