I tried to upgrade my First Aid skill since I didnt use it while leveling and Doctor Gregory Victor (the Trauma Surgeon in Arathi Highlands) wont give me the quest.
You need to be level 35 and have 225 in First Aid to start the "Triage" quest. I have both. But it simply isnt there. If I interact with the quest giver he will say:
"You have learned all that I am able to teach you at this time, Doctor [Name]. Return to me when your practice has expanded and I shall train you in the ways of the more advanced medicinal arts."