That's my eldest to a T. Diet helps us enormously, it's a lot of work, but less work than she is off the diet :-). She's still very full on but it's somehow more manageable, so the effort of the diet is SO worth it. I am on my phone and can't post a link easily, so google RPAH elimination diet and / or sue dengate.

I found keeping her busy with lots of play dates and out door time was key at that age. Before she was in school we had a major outing every morning (zoo, museum, swimming, aquarium all happened every week) and then errands and play ground or play dates every afternoon.