I recommend finding a therapist who specializes in gifted children. If you happen to be in the Portland OR area, PM me and I'll recommend one.
This seems like the way to go; the sooner the better, because it can take a while to get in with any dr for diagnosis, and then any therapist for treatment, but don't give up if you find many doctors are full or not taking insurance, or take 2 or more months to get an appointment. Get a list from your insurance (if applicable) and just slog through it.
Letting your child know you've made the appointment and that there is good prognosis for getting help at an early age should give reason for optimism.
And yes read up on why this might be occurring for your child. My ds was diagnosed with depression at age 9 or so, however has made a full recovery quickly with good treatment; so far no recurrence (now 16).
He does suffer some with anxiety still and we just try to keep good tabs on his mood, diet, exercise, etc. and get him back to a dr if needed.
