I'm going to have to agree with everyone else. Sugar probably isn't the only culprit. Studies have shown that food dyes, preservatives and artificial sugars (HFCS, aspartame, etc.) make kids way more crazy than naturally occuring sugars, like in fruit. My brother had major ADHD -- still does as a 33 year old, actually -- and he could handle natural sugars, but processed food put him over the edge.
If it was me, I'd cut out all processed junk foods. Read labels. If you don't know what a word means, don't offer it to your child. For breakfast, offer a non-sugar cereal like Cheerios and milk plus a banana. Snack could be cashews and apple slices. Lunch could be a turkey sandwich with tomato and green beans on the side. Afternoon snack of pretzels and hummus. For dinner, offer chicken and rice plus carrots and strawberries. Those are all foods a three year old can eat. She'll get natural sugar from the milk, banana, apples, carrots and strawberries, but no preservatives or food dyes.
Try that for a few weeks -- it will take longer than a week, and see if her behavior changes.