Maybe try making her rice a little more starchy and roll it into balls for her so she can use her fingers?
I have a big tin of crackers and let DS choose which he wants, the variety excites him and makes him feel like it's special even though it's just crackers.
DS won't entertain any kind of rice, cous cous, anything bitty. I usually make meals to suit him but if I make curry with rice for example I give him a side of some sort of bread, not our regular multigrain sliced bread but chapati, naan (all different flavours), tortilla, garlic bread, chiabata, those various flavours of tear and share bread from the bakery etc. Maybe she'd go for a different type of bread?
Does she use a fork yet? I tend to choose pasta that DS can stab reasonably easily with his fork to avoid frustration.
Like pp said starchy veg, oven baked chips/wedges made from turnip, sweet pot etc.
If carbs at meal times is really a no go then I'd offer some carbs snacks, pancakes, oaty chews, mini muffins, sugar free cake etc. There are recipes on the weaning recipe board for sugar free versions. Things like sweet potato mini muffins you get the carbs of the sweet pot as well as the flour, or can split it with oats too.
Another thing to consider is she might be self regulating, maybe she doesn't need so much carbs just now.