Don't let the pediatrician try to diagnose. He/she simply doesn't have the necessary expertise and you want this done right. Ask for a referral to a specialist like a child psychiatrist. A specialist will give you forms to fill out, as well as some for your daughter's teacher. Those will get assessed, along with any previous medical reports about related problems, and you'll meet with the psychiatrist to discuss the symptoms.
Be prepared for a wait. It can take months to get in with a specialist, so don't delay in asking the pediatrician for the referral.
Our process was a long one. I mentioned my concerns about our son's behavior to his pediatrician (ADHD is one of his specialties) and he immediately sent us to a child psychologist (who can't diagnose, but offers feedback). We got behavior modification strategies, none of which worked. So, the psychologist referred us to a behavioral therapist (also not qualified to diagnose but offers feedback). More strategies that didn't work, since our son couldn't control his behavior. Then we saw a child psychiatrist, who could diagnose and offer medication, if necessary.
You are right in that diet and parenting can't fix ADHD. It would be wonderful if that was the case! It really is a medical issue and a complex one at that.
Medication, combined with therapy, has the best track record for treatment. Be very careful about any "alternative" strategies peddled by the general public. You want to build your own knowledge of this condition and listen to the specialists, if you do, in fact, get this diagnosis for your daughter. Two great resources are CHADD and ADDitude magazine. Also look for message boards online devoted strictly to ADHD so you can avoid the general public, which generally tends to be extremely misinformed about ADHD.
Best of luck as you start the process!