That is odd that your psychiatrist is resistant to stimulant medications at his age. You might seek a second opinion, because it is quite common practice, and the stimulants will have the same kind of effect, only more predicatble, and longer lasting. Strattera may be the drug your psychiatrist is talking about, it is a non stimulant ADHD medication, but it does aid in inattention and is not nearly as effective for my child as a stimulant is for controling hyperactivity, so I would say at least one kid does just the opposite of what your psychiatrist told you. Worth a look at someone elses opinion, since it seems a little far off what most of us have heard from psychiatrists.
Many untreated adults with ADHD drink coffee or soda and chain smoke to self medicate, so there is a long history of using caffine. You could also try viviran or nodose, but I would talk to the doctor about all of it first. I think I have even seen cafinated water somewhere!
You saw what most of us see, that it is not our imagination, it is not red food coloring, it is not her diet, and it is not your parenting, it is how her brain funcitons. Getting her on the right dosages of the right meds once she is old enough if you stick with this psychiatrist and it will make even more of a difference.