I dunno. Pediatricians already ask all the "Are they doing X?" type questions to screen for delays. That seems to be a frequent point at which parents get the idea that these kids are more than a bit ahead of the curve. My pediatrician "diagnosed" DS8 as HG+ at 15 months old when DS was naming parts of the body using the official medical terms like clavicle and knew all the colors in the big crayon box.
It doesn't seem like a big stretch. Granted, however, I have a ped that is really on the ball...
I'll add that peds have two other things going for them. Most are pretty bright themselves, and they have no specific axe to grind about education. For teachers, IDing a GT kid means more work for them. For a doctor, it's not necessarily anything more than something to write on the chart. It seems like a more neutral forum.
