Although I'm not a celiac, I grew up on a gluten free diet so nearly all of my childhood breakfasts were based on short grain brown rice. My favorite was what we called "muesli" even though it didn't really resemble any muesli you can buy in a store.
Basically I'd start with a bowl of cold cooked short grain brown rice (we always had some in the fridge, it was an ongoing thing) and I'd add to it every kind of dried or fresh fruit that we had in the house at the time, chopped of course, along with an assortment of toasted nuts and seeds (we often had a mixed container of that on the go as well).
Of course each muesli would be a little different and that was part of the allure. The most common dried fruits in my bowl would be raisins, apricots and dates, while the fresh ones were banana, peach, pear, and strawberries when they were in season. It was always super yummy and fun, and very healthy no doubt. Nuts and seeds that worked well were cashews, flaked almonds, shredded coconut and sesame seeds. I'm sure sunflower seeds would be great too but I've never liked those.
A much simpler version of this was more commonly eaten in our household, and that's rice, chopped banana and raw or toasted cashew nuts. Very quick and easy and really tasty. When I was little I was only allowed to use half a banana in my bowl because of the sugar content (I was hypoglycemic) but as I got older I would tend to sneak a full banana in (much nicer!).
Chopped dates, coconut and milk with the rice was another childhood favorite. I think the milk mellowed the sweetness of the dates a bit, and also made it seem more like "normal people's" cereal.
I hope my remembrances will prove helpful to someone.... really I think creativity is the order of the day when it comes to breakfast, whether you eat gluten-free or not!