The dairy should be eliminated completely for a few weeks at least. It can be hard to tell what food is causing symptoms at first. Dairy is a known problem for many people, even those who don't have celiac disease. Carbs are bad if you are having digestive upset and bloating. The carbs feed the bacteria that make gas in your gut and that can cause symptoms. Everybody is an individual though so you may not have bad symptoms. But when you are trying to heal fast and aren't sure what's causing the problems, eliminating some common problem foods makes sense. There is no reason to reduce the dairy and carbs slowly though. They can be cut out completely right away. You should be able to tell if it's helping within a week or so. Eliminating them is no problem as long as you don't blow away!
I think it won't hurt a bit to eliminate dairy for a while. As far as carbs, that's kind of an individual thing. Some do better without them or with limiting them and some, like myself, have to have carbs. I am skinny, have a high metabolism & would dry up & blow away without my carbs & I eat lots of carbs. They don't bother me.
Keeping a food & symptom log can be a great help especially in the beginning.